courses › Mental Arithmetic

Division

level 6 course

Division as a missing factor, then bigger exact divisions.

Best in your head · no pen, no calculator why?

Opens at level 6.

Builds on: Times tables (not open yet)

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

Division undoes multiplication. 56 ÷ 8 asks: 8 times what makes 56? So every times-table fact you know is also a division fact.

Bigger divisions come down to small ones. You can cross the same zeros off both numbers, or split a big number into pieces that divide cleanly.

Dividing by a number below 1 makes the answer bigger. 10 ÷ 0.5 asks how many halves fit in 10, and there are 20 of them.

Techniques

Missing factor, then zeros

Any exact division, including numbers that end in zeros.

Read 56 ÷ 8 as 8 × ? = 56. The missing factor is the answer.
If both numbers end in zeros, cross the same number of zeros off each.
Find the fact that fits the front digits. In 3,000 ÷ 6, that is 30 ÷ 6 = 5.
Each zero after those digits goes on the end of the answer: 500.

worked example

Example: 3,500 ÷ 70

Cross one zero off each: 350 ÷ 7.
35 ÷ 7 = 5, and one zero is left: 50.

Answer: 50

Split the number into pieces

Dividing by 6 to 15 when the answer is between 10 and 30.

Take out 10 lots of the divisor, or 20 lots if that still fits.
Divide what is left with a fact.
Add the two answers.

worked example

Example: 195 ÷ 13

10 × 13 = 130, so split 195 into 130 + 65.
130 ÷ 13 = 10, and 65 ÷ 13 = 5.
10 + 5 = 15.

Answer: 15

Count halves and quarters

Dividing by 0.5 or 0.25.

÷ 0.5 asks how many halves fit. Each whole holds 2, so double the number.
÷ 0.25 asks how many quarters fit. Each whole holds 4, so multiply by 4.
Check the size: the answer is bigger than the number you started with.

worked example

Example: 13 ÷ 0.25

Each whole holds 4 quarters.
13 × 4 = 52.

Answer: 52

Tips by skill

TipDivision facts: Turn it into a times fact: the second number times what gives the first?
TipDivide with zeros: Cross the same number of zeros off both. Use the fact that fits the front digits; any zeros after them go on the answer.
TipSplit the dividend: Take out 10 or 20 lots of the divisor first, divide the rest, then add the two answers.
Tip÷ 0.5 and ÷ 0.25: ÷ 0.5 doubles the number and ÷ 0.25 multiplies it by 4, because each whole holds 2 halves or 4 quarters.

Watch out for

Mixing up which number divides. 56 ÷ 8 asks how many 8s make 56, which is 7.
Cancelling a zero from only one number. 2,400 ÷ 60 becomes 240 ÷ 6, not 2,400 ÷ 6.
Dividing the leftover and forgetting the first piece. 156 ÷ 12 is 10 from the 120, plus 3 from the 36.
Dividing by 4 when the question says ÷ 0.25. That gives 4.5 for 18 ÷ 0.25, instead of 72.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

Division facts par 3 s not tried yet
worked example
16 ÷ 8

Answer: 2
1. Read it as a missing factor: 8 × ? = 16. Since 8 × 2 = 16, the answer is 2.
Divide with zeros par 7 s not tried yet
worked example
120 ÷ 60

Answer: 2
1. Cancel a zero from both numbers: 120 ÷ 60 = 12 ÷ 6.
2. 12 ÷ 6 = 2, because 6 × 2 = 12.
Split the dividend par 7 s not tried yet
worked example
225 ÷ 15

Answer: 15
1. Split 225 into 150 + 75.
2. 150 ÷ 15 = 10 and 75 ÷ 15 = 5, so the answer is 15.
÷ 0.5 and ÷ 0.25 par 7 s not tried yet
worked example
35 ÷ 0.25

Answer: 140
1. Dividing by 0.25 asks how many quarters fit. Each whole holds 4 quarters, so 35 × 4 = 140.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

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