Fluent multiplication and division facts
Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division
What a learner can do afterwards
- Answer any single-digit multiplication fact within 3 seconds
- Answer any related division fact within 3 seconds
- Use known facts to derive unknown facts (e.g. 9 × 7 from 10 × 7 − 7)
1 · Read
You already know your times tables. Being fluent means you do not stop to count on fingers or skip-count from the start. You just know the answer, fast. Aim to answer facts like 6 × 8 or 56 ÷ 8 in under three seconds.
Mia forgets 9 × 7 for a second. She knows 10 × 7 = 70. Since 9 is one less than 10, she takes away one 7: 70 − 7 = 63. So 9 × 7 = 63, without counting from zero.
Every multiplication fact comes with two division facts for free. If you know 8 × 6 = 48, you also know 48 ÷ 8 = 6 and 48 ÷ 6 = 8.
Fast recall or a quick known-fact trick both count as fluent. Either way, you get to the answer in seconds.
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Strategies for dividing
When you divide a number, you're really asking a multiplication question backward. If you see 48 ÷ 6, ask yourself: 6 times what number makes 48? You can count up by 6s (6, 12, 18, 24...) until you hit 48, or you can jump straight to a fact you already know, like 6 × 8 = 48. Both ways get you to the same answer: 8. The more multiplication facts you know by heart, the faster you can divide.
Ways to divide greater numbers
Bigger division problems get easier when you break them into smaller pieces you already know. To find 96 ÷ 8, you might think: 8 × 10 = 80, and I still need 16 more. 8 × 2 = 16. So 10 + 2 = 12 groups of 8.
Count by units of 9 to multiply
Skip counting by 9s (9, 18, 27, 36, 45...) helps you multiply fast, but there's an even quicker trick. Since 9 is one less than 10, you can multiply by 10 first and then subtract one group. For 9 × 6, think 10 × 6 = 60, then 60 − 6 = 54. Once you spot this pattern, every 9s fact gets easier.
Count by units of 7 to multiply and divide by using arrays and tape diagrams
An array is rows and columns of dots or squares that show a multiplication fact. A 7-by-4 array has 4 rows of 7 dots, which is 28 dots total: 7 × 4 = 28. That same array shows the division fact too. If you split 28 dots into rows of 7, you get 4 rows, so 28 ÷ 7 = 4.
Mental Division Strategy
Some numbers are easier to work with in your head than others. This is called using compatible numbers. If you need to divide and the numbers don't feel friendly, look for a nearby multiplication fact you already know well, and build from there instead of starting from scratch. The stronger your multiplication facts, the more division problems you can solve just by thinking.
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Optional connections
20 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.