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Therefore, its place value is 7 tens, which equals 70."},{"text":"7 hundreds or 700.","correct":false,"explanation":"This treats the 7 as though it were in the hundreds column. It is in the tens column, so its value is 7 tens, or 70."},{"text":"7 ones or 7.","correct":false,"explanation":"This ignores the position of the digit and uses its face value. The 7 occupies the tens column, so it is worth 70."},{"text":"7 thousands or 7,000.","correct":false,"explanation":"This confuses the 7 with the leftmost digit in the thousands column. The 7 is actually in the tens column and is worth 70."}]},{"id":"6ed80f4e-5249-4588-961a-977b4dbdaae1","cardType":"cloze","points":null,"front":"In $58.26$, the 5 is worth [ ] and the 2 is worth [ ].","back":"In $58.26$, the 5 is worth 50 and the 2 is worth two tenths.","mcqOptions":[{"text":"In $58.26$, the 5 is worth 50 and the 2 is worth two tenths.","correct":true,"explanation":"The 5 is in the tens column, making its value 50. The 2 is immediately after the decimal point, so it represents two tenths."},{"text":"In $58.26$, the 5 is worth 5 and the 2 is worth two tenths.","correct":false,"explanation":"This uses the face value of 5 instead of its place value. The 5 is in the tens column, so it is worth 50; the 2 is two tenths."},{"text":"In $58.26$, the 5 is worth 50 and the 2 is worth two hundredths.","correct":false,"explanation":"This places the 2 one decimal position too far right. As the first digit after the decimal point, it represents two tenths, while the 5 represents 50."},{"text":"In $58.26$, the 5 is worth 500 and the 2 is worth two hundredths.","correct":false,"explanation":"Both digits have been shifted one place to the left or right incorrectly. The 5 is worth 50, and the first decimal digit represents two tenths."}]},{"id":"ccf99bb9-cf09-433a-af55-0369793adeca","cardType":"basic","points":1,"front":"In a column method, what is the main alignment rule?","back":"Line up digits with the same place value.","mcqOptions":[{"text":"Line up digits with the same place value.","correct":true,"explanation":"Digits must be aligned by units, tens, hundreds and corresponding decimal places. This ensures that each column combines quantities with the same place value."},{"text":"Line up digits with the same digit.","correct":false,"explanation":"Matching identical digits does not preserve their values, because the same digit can occur in different columns. Digits must instead be aligned by place value."},{"text":"Line up digits by their left-hand edge.","correct":false,"explanation":"Aligning the left-hand edges can put units beneath tens when numbers have different lengths. Column methods require digits with the same place value to line up."},{"text":"Line up digits by their size.","correct":false,"explanation":"The visual or numerical size of individual digits does not determine their column. Digits must be aligned according to place value, such as units beneath units."}]},{"id":"6755a0ce-d991-44c7-88b4-627c48948cb7","cardType":"basic","points":1,"front":"If a column addition totals 10 or more, what should you do?","back":"Carry into the next column.","mcqOptions":[{"text":"Carry into the next column.","correct":true,"explanation":"A total of 10 or more contains an extra group of ten. Write the units digit in the current column and carry the remaining amount into the next column."},{"text":"Exchange from the next column.","correct":false,"explanation":"Exchanging from the next column is used in subtraction when the top digit is too small. In addition, a total of 10 or more must be carried."},{"text":"Write the total in the same column.","correct":false,"explanation":"Writing a two-digit total in one column destroys the place-value alignment. Write its units digit there and carry the tens digit into the next column."},{"text":"Ignore the tens digit.","correct":false,"explanation":"Ignoring the tens digit loses part of the total and makes the answer too small. The tens digit must be carried into the next place-value column."}]},{"id":"e98dae77-1236-4f3f-aff3-d977d31ee237","cardType":"cloze","points":null,"front":"Carrying changes [ ] of one place value into [ ] of the next place value.","back":"Carrying changes 10 of one place value into 1 of the next place value.","mcqOptions":[{"text":"Carrying changes 10 of one place value into 1 of the next place value.","correct":true,"explanation":"The base-ten system groups ten units of any place value into one unit of the next place value, such as 10 tens becoming 1 hundred."},{"text":"Carrying changes 100 of one place value into 1 of the next place value.","correct":false,"explanation":"This skips a place-value column by grouping one hundred at once. Carrying uses the base-ten relationship: 10 of one place value becomes 1 of the next."},{"text":"Carrying changes 10 of one place value into 10 of the next place value.","correct":false,"explanation":"This fails to convert between adjacent place values and would multiply the amount by ten. Instead, 10 units of one place value become 1 of the next."},{"text":"Carrying changes 1 of one place value into 10 of the next place value.","correct":false,"explanation":"This reverses the carrying relationship and describes moving towards a smaller place value. Carrying converts 10 of one place value into 1 of the next."}]},{"id":"78ecaa86-3d59-4d76-bee2-eb3568a704ac","cardType":"basic","points":2,"front":"Work out $368 + 74$.","back":"$442$","mcqOptions":[{"text":"$442$","correct":true,"explanation":"Adding the units gives $8+4=12$, so write 2 and carry 1. The tens then total 14, producing $368+74=442$."},{"text":"$432$","correct":false,"explanation":"This omits the carried 1 from the units calculation. Since $8+4=12$, that extra ten must be included, giving the correct total of $442$."},{"text":"$438$","correct":false,"explanation":"This adds only the 70 from 74 and leaves out its 4 units. Including both parts gives $368+70+4=442$."},{"text":"$452$","correct":false,"explanation":"This effectively counts an extra ten while carrying. After writing 2 from $8+4=12$, the tens total is 14, so the correct result is $442$."}]},{"id":"d865e263-8dcb-4847-9afe-34109936eca3","cardType":"basic","points":2,"front":"Work out $1475 + 206 + 93$.","back":"$1774$","mcqOptions":[{"text":"$1774$","correct":true,"explanation":"Adding by columns gives 14 units, 17 tens after carrying, and 7 hundreds after the next carry. Therefore, $1475+206+93=1774$."},{"text":"$1764$","correct":false,"explanation":"This omits the carried 1 from the units column when adding the tens. Including that extra ten makes the tens digit 7 and gives $1774$."},{"text":"$1674$","correct":false,"explanation":"This fails to carry the 1 from the tens column into the hundreds column. Including that carried hundred changes the total from $1674$ to $1774$."},{"text":"$1784$","correct":false,"explanation":"This counts the carry from the units column twice when adding the tens. It should be included once, producing a tens digit of 7 and a total of $1774$."}]},{"id":"6fb81353-153b-45bb-8af7-9583f8bb391c","cardType":"basic","points":1,"front":"In column subtraction, what should you do if the top digit is too small?","back":"Exchange from the next column.","mcqOptions":[{"text":"Exchange from the next column.","correct":true,"explanation":"Exchange one unit from the next place-value column for ten units in the current column. This makes the top digit large enough for the subtraction."},{"text":"Carry into the next column.","correct":false,"explanation":"Carrying into the next column is associated with addition totals of 10 or more. In subtraction, exchange from the next column when the top digit is too small."},{"text":"Subtract the top digit from the bottom digit.","correct":false,"explanation":"Reversing the subtraction in one column changes the calculation and can hide the need to exchange. Instead, exchange from the next column and keep the original order."},{"text":"Add 10 without changing the next column.","correct":false,"explanation":"Adding 10 without reducing the next column changes the number’s total value. Exchange correctly by adding 10 to the current column and subtracting 1 from the next."}]},{"id":"984abc47-c573-4982-9b83-cdb8bdcd0dee","cardType":"cloze","points":null,"front":"Exchanging [ ] gives [ ].","back":"Exchanging 1 ten gives 10 ones.","mcqOptions":[{"text":"Exchanging 1 ten gives 10 ones.","correct":true,"explanation":"A ten has the same value as ten ones, so it can be exchanged during subtraction without changing the total value."},{"text":"Exchanging 1 ten gives 100 ones.","correct":false,"explanation":"This confuses tens with hundreds. One ten is worth 10 ones; 100 ones would have the value of one hundred."},{"text":"Exchanging 1 one gives 10 tens.","correct":false,"explanation":"This reverses the place-value relationship and increases the value. The valid exchange is 1 ten for 10 ones, which preserves the total."},{"text":"Exchanging 10 tens gives 1 one.","correct":false,"explanation":"This reduces a value of one hundred to one, so it is not an equivalent exchange. One ten exchanges for 10 ones."}]},{"id":"15be6a5e-6f24-4a58-b483-1125f7e2e5cd","cardType":"basic","points":1,"front":"If 4 tens gives away 1 ten, how many tens remain?","back":"3 tens","mcqOptions":[{"text":"3 tens","correct":true,"explanation":"Giving away 1 ten from 4 tens leaves $4-1=3$ tens, which has a total value of 30."},{"text":"5 tens","correct":false,"explanation":"This results from adding the ten instead of giving it away. Subtracting 1 ten from 4 tens leaves 3 tens."},{"text":"2 tens","correct":false,"explanation":"This subtracts 2 tens rather than the single ten given away. The calculation is $4-1=3$, so 3 tens remain."},{"text":"3 ones","correct":false,"explanation":"The subtraction gives 3, but the place-value unit must remain tens. Therefore, 4 tens minus 1 ten leaves 3 tens, not 3 ones."}]},{"id":"7bd8bf41-19f3-49c0-af80-3e21aaffffa1","cardType":"basic","points":2,"front":"Work out $3740 - 526$.","back":"$3214$","mcqOptions":[{"text":"$3214$","correct":true,"explanation":"Subtracting in parts gives $3740-500=3240$, then $3240-26=3214$. This agrees with column subtraction using regrouping."},{"text":"$3224$","correct":false,"explanation":"This is 10 too large, indicating that only 1 ten was effectively subtracted instead of 2 tens. Correct regrouping gives $3740-526=3214$."},{"text":"$3314$","correct":false,"explanation":"This is 100 too large, indicating that 4 hundreds were effectively subtracted instead of 5 hundreds. The correct result is $3214$."},{"text":"$3204$","correct":false,"explanation":"This is 10 too small, caused by subtracting an extra ten during regrouping. Careful column subtraction gives $3740-526=3214$."}]},{"id":"6c5a0c06-817d-494c-9df3-bb10b2fdcf00","cardType":"cloze","points":null,"front":"For decimals, the first digit after the decimal point is [ ] and the second is [ ].","back":"For decimals, the first digit after the decimal point is tenths and the second is hundredths.","mcqOptions":[{"text":"For decimals, the first digit after the decimal point is tenths and the second is hundredths.","correct":true,"explanation":"Moving right from the decimal point, place values divide by 10 each time. The first position is tenths and the second is hundredths."},{"text":"For decimals, the first digit after the decimal point is units and the second is tenths.","correct":false,"explanation":"Units are immediately to the left of the decimal point, not after it. The first two positions to the right are tenths and hundredths."},{"text":"For decimals, the first digit after the decimal point is hundredths and the second is thousandths.","correct":false,"explanation":"This shifts both place values one position too far to the right. The first decimal digit represents tenths and the second represents hundredths."},{"text":"For decimals, the first digit after the decimal point is tenths and the second is thousandths.","correct":false,"explanation":"This skips the hundredths position. Decimal places progress from tenths to hundredths and then thousandths as they move right."}]},{"id":"0ac694fc-4f65-4468-88cf-dbb08f6c6484","cardType":"basic","points":1,"front":"What must be aligned vertically when adding or subtracting decimals?","back":"The decimal points.","mcqOptions":[{"text":"The decimal points.","correct":true,"explanation":"Aligning decimal points places digits of equal place value in the same columns, allowing units, tenths and hundredths to be combined correctly."},{"text":"The decimal digits.","correct":false,"explanation":"Matching digits without considering their place values can combine unlike quantities. The decimal points must align so units, tenths and hundredths form vertical columns."},{"text":"The first digits.","correct":false,"explanation":"Aligning the first digits can misalign place values when numbers have different lengths. The decimal points must be vertically aligned instead."},{"text":"The final digits.","correct":false,"explanation":"Aligning the final digits may place tenths beneath hundredths or units. Decimal points are aligned so corresponding place values share columns."}]},{"id":"8f887b7b-80d4-47cf-bd10-7fbc1a23b825","cardType":"basic","points":2,"front":"Why can placeholder zeros be added after a decimal point?","back":"They do not change the number’s value.","mcqOptions":[{"text":"They do not change the number’s value.","correct":true,"explanation":"Zeros written at the end of a decimal do not add any extra tenths, hundredths or thousandths, so the represented value remains unchanged."},{"text":"They always increase the number’s value.","correct":false,"explanation":"This confuses appending decimal zeros with multiplying by 10. A trailing zero changes the notation and place-value columns, but not the number’s value."},{"text":"They always decrease the number’s value.","correct":false,"explanation":"Adding trailing zeros does not divide the number or shift its decimal point. They leave the value unchanged while making decimal columns easier to align."},{"text":"They double the number’s value.","correct":false,"explanation":"A trailing placeholder zero does not perform multiplication. It simply shows an unused decimal place, so the number’s value stays the same."}]},{"id":"e92b4de7-f137-4cc5-a07a-3edbcdbbb8e6","cardType":"basic","points":2,"front":"Work out $58.26 + 4.87$.","back":"$63.13$","mcqOptions":[{"text":"$63.13$","correct":true,"explanation":"The hundredths sum to 13, carrying 1 tenth; the tenths then sum to 11, carrying 1 unit. The total is $63.13$."},{"text":"$62.13$","correct":false,"explanation":"This misses the carry from the tenths column into the units column. Including both carries gives $58.26+4.87=63.13$."},{"text":"$63.03$","correct":false,"explanation":"This omits the carried 1 from the hundredths column when adding the tenths. Correctly regrouping $6+7=13$ leads to $63.13$."},{"text":"$62.03$","correct":false,"explanation":"This omits both carries: one from hundredths to tenths and another from tenths to units. Including them produces the correct total of $63.13$."}]},{"id":"9fa2023f-7031-4eee-959f-be1952828645","cardType":"basic","points":2,"front":"For $72 - 18.6$, why write $72$ as $72.0$?","back":"It gives a tenths column.","mcqOptions":[{"text":"It gives a tenths column.","correct":true,"explanation":"Writing $72$ as $72.0$ leaves its value unchanged while providing a tenths digit to align with the tenths digit in $18.6$."},{"text":"It gives a hundredths column.","correct":false,"explanation":"Writing one zero after the decimal creates a tenths place, not a hundredths place. Two decimal digits would be needed to show a hundredths column."},{"text":"It gives a decimal-point column.","correct":false,"explanation":"The decimal point separates whole and fractional parts but is not itself a place-value column. Writing $72.0$ provides a tenths column for alignment."},{"text":"It gives a units column.","correct":false,"explanation":"The original number already has a units column containing 2. The added zero creates a tenths column so the decimal places align correctly."}]},{"id":"c2659d4c-ceb4-49fa-a0e1-a271b86fe394","cardType":"basic","points":2,"front":"Work out $72 - 18.6$.","back":"$53.4$","mcqOptions":[{"text":"$53.4$","correct":true,"explanation":"Aligning the decimal points gives $72.0-18.6$. Borrowing across the decimal leaves $53.4$, so the subtraction has been carried out correctly."},{"text":"$54.4$","correct":false,"explanation":"This results from borrowing incorrectly in the units column. Writing $72$ as $72.0$ and subtracting $18.6$ carefully gives the correct answer, $53.4$."},{"text":"$53.6$","correct":false,"explanation":"This comes from subtracting the decimal digits without borrowing correctly. Since $72.0-18.6=53.4$, the correct difference is $53.4$."},{"text":"$54.0$","correct":false,"explanation":"This treats $18.6$ too much like $18$ and loses the effect of the decimal part. Correctly aligning place values gives $72.0-18.6=53.4$."}]},{"id":"53ffa5a1-c49d-4e7f-a2a1-2113fbb06376","cardType":"cloze","points":null,"front":"Money is normally written to [ ] because [ ] make £1.","back":"Money is normally written to two decimal places because 100 pence make £1.","mcqOptions":[{"text":"Money is normally written to two decimal places because 100 pence make £1.","correct":true,"explanation":"One pound contains 100 pence, so pounds and pence are represented using two digits after the decimal point. Money is therefore normally written to two decimal places."},{"text":"Money is normally written to one decimal place because 10 pence make £1.","correct":false,"explanation":"This confuses pounds with a decimal system based on tenths. There are 100 pence in £1, so money is normally written to two decimal places."},{"text":"Money is normally written to three decimal places because 1000 pence make £1.","correct":false,"explanation":"This incorrectly treats each pound as containing 1000 smaller units. A pound contains 100 pence, which is why money is normally written to two decimal places."},{"text":"Money is normally written to two decimal places because 10 pence make £1.","correct":false,"explanation":"Although the number of decimal places is correct, the conversion is not: 10 pence is £0.10. There are 100 pence in £1."}]},{"id":"3d419577-7629-4950-847e-4eb7a237ae9a","cardType":"basic","points":1,"front":"How should £6.5 usually be written as a final money answer?","back":"£6.50","mcqOptions":[{"text":"£6.50","correct":true,"explanation":"Money amounts are normally written with two decimal places because there are 100 pence in a pound. The zero shows that the amount includes 50 pence."},{"text":"£6.05","correct":false,"explanation":"This places the digit 5 in the hundredths column, making the amount six pounds and five pence. £6.5 means six pounds and fifty pence, written £6.50."},{"text":"£6.500","correct":false,"explanation":"This adds an unnecessary third decimal place. Standard money notation uses two decimal places, so the amount should be written as £6.50."},{"text":"£7.00","correct":false,"explanation":"This incorrectly changes the value by rounding to the nearest pound. The original amount includes 50 pence, so it should be written as £6.50."}]},{"id":"f5e0b527-dc94-444b-b09f-cfda8e3c84f7","cardType":"basic","points":2,"front":"A book costs £18.76 and you pay with £40. What is the change?","back":"£21.24","mcqOptions":[{"text":"£21.24","correct":true,"explanation":"Change is found by subtracting the cost from the amount paid: $£40.00-£18.76=£21.24$. The answer is correctly written to two decimal places."},{"text":"£22.24","correct":false,"explanation":"This comes from an incorrect borrow when subtracting the pence and pounds. Correct column subtraction gives $£40.00-£18.76=£21.24$."},{"text":"£21.76","correct":false,"explanation":"This retains the 76 pence from the cost instead of subtracting it from £1 during borrowing. The correct change is $£40.00-£18.76=£21.24$."},{"text":"£58.76","correct":false,"explanation":"This adds the cost to the payment rather than finding the difference. Change is calculated by subtraction, so $£40.00-£18.76=£21.24$."}]},{"id":"aec0734c-dc1f-4fa0-a6ef-45f6ad080768","cardType":"basic","points":1,"front":"For a calculation containing only addition and subtraction, what is a safe method?","back":"Work from left to right.","mcqOptions":[{"text":"Work from left to right.","correct":true,"explanation":"Addition and subtraction have equal priority, so a calculation containing only these operations is evaluated in order from left to right."},{"text":"Work from right to left.","correct":false,"explanation":"Working right to left reverses the required order and can change the result because subtraction is not commutative. Addition and subtraction should be performed from left to right."},{"text":"Do all addition first.","correct":false,"explanation":"Addition does not take priority over subtraction; the two operations have equal precedence. Without brackets, they should be carried out from left to right."},{"text":"Do all subtraction first.","correct":false,"explanation":"Subtraction does not take priority over addition; both operations have equal precedence. A calculation containing only addition and subtraction should be worked from left to right."}]},{"id":"0d163fd6-b41e-4e1c-b2da-b317cac38e78","cardType":"cloze","points":null,"front":"In a longer calculation, the sign before a number [ ].","back":"In a longer calculation, the sign before a number belongs with that number.","mcqOptions":[{"text":"belongs with that number","correct":true,"explanation":"The sign determines whether that particular number is added or subtracted. Keeping each sign attached to its number helps prevent sign errors when rearranging or calculating."},{"text":"can be ignored during working","correct":false,"explanation":"Ignoring the sign changes whether the number is added or subtracted, often changing the answer substantially. The sign belongs with the number immediately following it."},{"text":"belongs with the previous number","correct":false,"explanation":"A sign applies to the number that follows it, not the preceding number. Treating it as part of the previous term commonly causes errors in longer calculations."},{"text":"always means subtract that number","correct":false,"explanation":"A plus sign means the following number is added, while a minus sign means it is subtracted. Therefore, the sign belongs with that number rather than always indicating subtraction."}]},{"id":"23aeec1b-ffbb-44e1-9e94-6f93149240d1","cardType":"basic","points":3,"front":"Work out $64.5 - 18.23 - 7.4 + 25$.","back":"$63.87$","mcqOptions":[{"text":"$63.87$","correct":true,"explanation":"Working from left to right gives $64.5-18.23=46.27$, then $46.27-7.4=38.87$, and finally $38.87+25=63.87$."},{"text":"$78.67$","correct":false,"explanation":"This treats the subtraction of $7.4$ as addition, reversing its sign. Keeping the sign with each number and working left to right gives $63.87$."},{"text":"$70.53$","correct":false,"explanation":"This misaligns $7.4$ as though it were $0.74$. Writing it as $7.40$ and aligning decimal points correctly gives the final answer $63.87$."},{"text":"$13.87$","correct":false,"explanation":"This subtracts the final $25$ instead of adding it, reducing the result by $50$ overall. Following the signs correctly gives $63.87$."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Addition and Subtraction","title":"Addition and Subtraction Flashcards","topbar":{"backHref":"/igcse/maths/edexcel/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"8c271d26-65e8-4f4e-a8b3-222016724818","walled":"$L39"}],"$L3a","$L3b"]