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Equations with a box

Boxes & letters in expressions

Japanese school year: Elementary 3

What you learn

Students learn to express mathematical situations into equations using a box symbol for unknown numbers and solve them using inverse operations. This approach is helpful for finding missing quantities or differences in costs. A clear understanding of basic four arithmetic operations is essential before beginning.

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Key points

When an added number is unknown, subtract the known number a from the sum b to find □.

□+a=b  ⟺  □=b−a\square + a = b \iff \square = b - a

When the subtracted number is unknown, subtract the remaining b from the start a to find □.

a−□=b  ⟺  □=a−ba - \square = b \iff \square = a - b

When a factor is unknown, divide the product b by the known number a to find □.

□×a=b  ⟺  □=b÷a(a≠0)\square \times a = b \iff \square = b \div a \quad (a \neq 0)

When the divisor is unknown, divide the starting number a by the answer b to find □.

a÷□=b  ⟺  □=a÷b(b≠0)a \div \square = b \iff \square = a \div b \quad (b \neq 0)

Choose a set to practice.