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Relate multiplication and division

Multiplication and division are inverse operations describing the same equal-groups or array relationship: from a×b=ca \times b = c, the related division equations c÷a=bc \div a = b and c÷b=ac \div b = a identify the total, number of groups, and group size. This connection supports finding unknown factors or quotients and checking results within whole-number facts and division situations involving totals up to 100; fractions, negative numbers, and generalized algebraic treatment are not included.

Detailed Explanation: Relate multiplication and division

Multiplication and division are inverse operations. They describe the same equal-groups situation in different ways.

If

a×b=c,a \times b = c,

then the related division facts are

c÷a=bandc÷b=a.c \div a = b \qquad\text{and}\qquad c \div b = a.
  • cc is the total.
  • One factor tells the number of groups.
  • The other factor tells the number in each group.

Example: There are 2424 apples placed equally into 44 baskets. How many apples are in each basket?

  1. Use multiplication to describe the equal groups:

4×6=24 4 \times 6 = 24

This means 44 groups of 66 make 2424.

  1. Use division to find the number in each basket:

24÷4=6 24 \div 4 = 6

So, each basket has 66 apples.

  1. The other related division fact is:

24÷6=4 24 \div 6 = 4

This tells us that 2424 apples make 44 groups when there are 66 apples in each group.

The related facts are:

4×6=24,6×4=244 \times 6 = 24,\qquad 6 \times 4 = 24 24÷4=6,24÷6=424 \div 4 = 6,\qquad 24 \div 6 = 4

Use the multiplication fact to check a division answer: since 4×6=244 \times 6 = 24, the answer to 24÷424 \div 4 is 66.

Learn by doing: Relate multiplication and division

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