Number Operations Flashcards

All 44 cards in this deck

What do the symbols $<$ and $>$ mean?

$<$ means 'less than', $>$ means 'greater than'.
e.g. $14 < 21$

What do the symbols $\le$, $\ge$ and $\ne$ mean?

'Less than or equal to', 'greater than or equal to', 'not equal to'.

What is the inverse operation of multiplying by 6?

Dividing by 6.

What is the reciprocal of a number?

e.g. the reciprocal of 20

1 divided by the number.
e.g. $\frac{1}{20}$, or $0.05$

True or false? $8 - 3$ gives the same answer as $3 - 8$.

False. Addition and multiplication can be done in any order, but subtraction and division cannot.

What are the steps to check a subtraction using the inverse operation?

e.g. check $645 - 500 = 145$

1. Take your answer: $145$
2. Add back the number you subtracted: $145 + 500$
3. It should give the number you started with: $645$ ✓

What does BIDMAS stand for?

Brackets, Indices, Division, Multiplication, Addition, Subtraction.

In the order of operations, which comes first: multiplication or division?

Neither — do them left to right. The same applies to addition and subtraction.

Where does a square root come in the order of operations?

With indices — after brackets, before multiplying and dividing.

True or false? To work out $10 \times (3 + 5)$ you multiply first.

False. Brackets come first: $3 + 5 = 8$, then $10 \times 8 = 80$.

What are the steps to work out a calculation using BIDMAS?

e.g. $2 + 3 \times 4^2$

1. Indices first: $4^2 = 16$
2. Then multiply: $3 \times 16 = 48$
3. Then add: $2 + 48 = 50$

What are the steps to insert a pair of brackets to make a calculation correct?

e.g. $30 \div 3 + 2 - 4 = 2$

1. Work out what BIDMAS gives with no brackets: $10 + 2 - 4 = 8$, too big
2. Bracket a pair so a lower-priority step happens first: $30 \div (3 + 2)$
3. Check: $6 - 4 = 2$ ✓

What is the value of the 7 in the number 3721?

700 (7 hundreds).

What is the value of the 9 in the number 27.963?

0.9 (nine tenths).

What are the names of the first three decimal places, after the decimal point?

Tenths, hundredths, thousandths.

What are the steps to put decimals in order, smallest first?

e.g. $0.32$, $0.4$, $0.309$

1. Give them all the same number of decimal places: $0.320$, $0.400$, $0.309$
2. Compare digits from the left
3. Write the original numbers in order: $0.309$, $0.32$, $0.4$

True or false? $0.4$ is smaller than $0.35$ because 4 is smaller than 35.

False. $0.4 = 0.40$, which is greater than $0.35$.

True or false? $-3 > -5$

True. $-3$ is further right on the number line, so it is greater.

What is the rule for multiplying or dividing two negative numbers?

The answer is positive.
e.g. $-3 \times -4 = 12$

What is the rule for multiplying or dividing a negative number by a positive number?

The answer is negative.
e.g. $-20 \div 5 = -4$

What does subtracting a negative number do?

e.g. $6 - (-4)$

It is the same as adding: $6 + 4 = 10$.

What does adding a negative number do?

e.g. $8 + (-3)$

It is the same as subtracting: $8 - 3 = 5$.

What are the steps to find the difference between two temperatures when one is negative?

e.g. $-3\,^\circ$C and $5\,^\circ$C

1. Subtract the lower from the higher: $5 - (-3)$
2. Subtracting a negative means add: $5 + 3$
3. Difference $= 8\,^\circ$C

True or false? An answer of £4.5 should be written as £4.05.

False. It is £4.50 — money in pounds is written with two decimal places.

What are the steps to work out change from a note?

e.g. buy 2 cakes at £1.30 each, pay with £5

1. Find the total cost: $2 \times 1.30 =$ £$2.60$
2. Subtract from the amount paid: $5 - 2.60$
3. Change $=$ £$2.40$

What are the steps to add decimals using column addition?

e.g. $12.5 + 3.75$

1. Line up the decimal points, filling gaps with zeros: $12.50$ and $03.75$
2. Add from the right, carrying where needed
3. Bring the decimal point straight down: $16.25$

What are the steps to subtract using column subtraction with exchanging?

e.g. $503 - 147$

1. Line up the place value columns
2. If the top digit is too small, exchange from the next column left
3. Subtract each column right to left: $356$

True or false? To add $12.5 + 3.75$ in columns you line up the last digits on the right.

False. You line up the decimal points (the place value columns).

Which operation do the words 'sum', 'total' and 'altogether' tell you to use?

Addition.

Which operation does the word 'difference' tell you to use?

Subtraction — subtract the smaller number from the larger.

What are the steps of long multiplication?

e.g. $74 \times 58$

1. Multiply by the units: $74 \times 8 = 592$
2. Multiply by the tens: $74 \times 50 = 3700$
3. Add the lines: $4292$

What are the steps to multiply two decimals?

e.g. $54.6 \times 4.3$

1. Ignore the decimal points: $546 \times 43 = 23478$
2. Count the decimal places in the question: $1 + 1 = 2$
3. Put the point in the answer: $234.78$

What are the steps to divide by a decimal?

e.g. $7.2 \div 0.4$

1. Multiply both numbers by 10 (or 100) to make the divisor a whole number: $72 \div 4$
2. Do the division: $18$

In short division of a decimal by a whole number, where does the decimal point go in the answer?

e.g. $9.36 \div 4$

Directly above the decimal point in the number being divided: $2.34$.

In a problem asking the greatest number of items that can be bought, what do you do with the remainder?

Ignore it — round down to the whole number.
e.g. $23 \div 4 = 5.75$, so 5 items

True or false? Multiplying a number always makes it bigger.

False. Multiplying by a number less than 1 makes it smaller, e.g. $8 \times 0.5 = 4$.

What are the steps to use a given calculation to answer a related one?

e.g. given $34 \times 26 = 884$, find $3.4 \times 2.6$

1. Check the digits are the same: $34$ and $26$ ✓
2. Count the decimal places in the new question: $1 + 1 = 2$
3. Put the point in the same digits: $8.84$

Given that $1081 \div 23 = 47$, what is $108.1 \div 23$?

$4.7$ — the number being divided is 10 times smaller, so the answer is too.

Given that $23 \times 47 = 1081$, what is $230 \times 47$?

$10\,810$ — one factor is 10 times bigger, so the answer is 10 times bigger.

Given that $23 \times 47 = 1081$, is it true that $2.3 \times 47 = 10.81$?

False. Only one number was divided by 10, so the answer is $108.1$.

What does it mean to list possibilities systematically?

Writing them in a fixed order (e.g. smallest first) so none are missed or repeated.

How do you count the number of combinations when choosing one item from each of two lists?

e.g. 3 starters and 4 main courses

Multiply the numbers in the lists: $3 \times 4 = 12$ combinations.

How do you make the largest possible 3-digit number from a set of digits?

e.g. from 7, 3, 4, 9

Put the largest digits first, in decreasing order: $974$.

True or false? Using the digits 0, 3 and 7, '03' counts as one of the two-digit numbers.

False. A two-digit number cannot start with 0.