OCR GCSE Mathematics

## Place value and the four rules An **integer** is a whole number, positive, negative or zero. Each digit is worth ten times the digit to its right, so in $52\,318$ the 2 stands for 2 thousands and the 3 for 3 hundreds. Place value is what makes columns work in written addition and subtraction, and it is why multiplying by 10 moves every digit one place to the left. Adding and subtracting whole numbers by column means lining up digits of the same value and carrying or exchanging when a column runs over or runs short. Both are also worth doing mentally by adjusting to an easier number and correcting afterwards: $$ \begin{aligned} 347 - 98 &= 347 + 2 - 100 \\ &= 249 \end{aligned} $$ Here 98 was rounded up to 100, which takes away 2 too much, so 2 is added back. ### Long multiplication Multiply by each digit of the second number in turn, taking care with place value, then add the results. For $468 \times 37$ the 3 is really 30: $$ \begin{aligned} 468 \times 37 &= 468 \times 30 + 468 \times 7 \\ &= 14\,040 + 3\,276 \\ &= 17\,316 \end{aligned} $$ ### Long division Long division finds how many times the divisor goes into each successive part of the number. To work out $3\,588 \div 12$, 12 goes into 35 twice (24) leaving 11; bring down the 8 to make 118, and 12 goes into 118 nine times (108) leaving 10; bring down the 8 to make 108, and 12 goes into 108 nine times exactly. So $3\,588 \div 12 = 299$. When a remainder is left over it can be written as a remainder, as a fraction of…