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S.2 Write division sentences for arrays

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What are division arrays?

Division arrays are organized, equal rows of objects that help us see division as fair sharing or repeated subtraction.

Example:
  • 12 dots arranged in 3 equal rows show 12 ÷ 3 = 4.
  • Each row has 4 dots, so the quotient is 4.
Note

An array is always rectangular. The total number of objects is called the dividend, and the number of rows is the divisor.

Writing division sentences from arrays

To write a division sentence, first count the total number of objects. Then, decide if you are dividing by the number of equal rows or the number of equal columns. The sentence shows how the total is shared into equal groups.

Steps:
  • Look at the array:
  • Total objects (dividend): 8
  • Number of equal columns (divisor): 4
  • Division sentence: 8 ÷ 4 = 2
  • Meaning: 8 objects split into 4 equal columns gives 2 in each column.
Remember

You can write a division sentence for the rows OR the columns. Always check your answer by multiplying the divisor and the quotient. They should equal the dividend: 4 columns × 2 in each = 8 total.

Finding the quotient in array division

The quotient is the answer to a division problem. In an array, it tells how many objects are in each equal row or column.

Example:
  • An array shows 20 stars in 4 rows.
  • To find the quotient, ask: "20 divided into 4 equal groups gives how many in each group?"
  • 20 ÷ 4 = 5. The quotient is 5.
Note

The quotient will never be larger than the dividend. If you are dividing a number up to 50, your quotient will be 50 or less.

Using rows and columns in arrays

Arrays can be read by rows (horizontal groups) or by columns (vertical groups). Both ways lead to correct division sentences.

Example:
  • A 6 by 4 array has 24 objects total.
  • By Rows: 24 ÷ 6 = 4 objects in each row.
  • By Columns: 24 ÷ 4 = 6 objects in each column.
Note

Whether you use rows or columns depends on the problem. Always identify what the equal groups are meant to be.

Solving real-world array problems

We use array division to solve problems about arranging items into equal groups, like placing chairs in rows or sharing supplies.

Examples:
  • "Ms. Lee has 30 books. She places them equally on 5 shelves. How many books are on each shelf?" 30 ÷ 5 = 6
  • "A gardener plants 48 flowers in 6 equal rows. How many flowers are in each row?" 48 ÷ 6 = 8
Note

In word problems, the total amount is the dividend. The number of groups you are making is the divisor.