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How can these models be used to find the sum 2.3 + 1.94?



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The models show a total of 3 wholes,
tenths, and
hundredths. After regrouping 10 tenths into 1 whole, there are
wholes,
tenths, and
hundredths. Therefore, the sum of the numbers is
.
First row. Two large squares, each divided into a 10 by 10 grid of 100 small squares. Three columns, each divided into 10 small squares. Second row. One large square divided into a 10 by 10 grid of 100 small squares. Nine columns, each divided into 10 small squares. Four small squares.

1 answer

To find the sum \( 2.3 + 1.94 \) using models, let's break it down step by step.

  1. Visual Representation:

    • The number 2.3 can be represented as:
      • 2 wholes (two large squares)
      • 3 tenths (three columns of small squares).
    • The number 1.94 can be represented as:
      • 1 whole (one large square)
      • 9 tenths (nine columns of small squares)
      • 4 hundredths (four small squares).

  2. Adding the two numbers:

    • Wholes:
      • \( 2 + 1 = 3 \) wholes.
    • Tenths:
      • \( 3 + 9 = 12 \) tenths.
    • Hundredths:
      • There are 4 hundredths from \( 1.94 \).

  3. Regrouping:

    • Since 10 tenths make 1 whole, we can regroup:
      • From the 12 tenths, we can take 10 tenths and turn it into 1 whole.
      • That leaves us with \( 2 \) tenths (since \( 12 - 10 = 2 \)).
      • Therefore, the total number of wholes becomes:
        • \( 3 + 1 = 4 \) wholes.

  4. Final Count:

    • After regrouping, we have:
      • Wholes: 4
      • Tenths: 2
      • Hundredths: 4

Thus, the filled in parts are:

  • The models show a total of 4 wholes, 2 tenths, and 4 hundredths. After regrouping 10 tenths into 1 whole, there are 4 wholes, 2 tenths, and 4 hundredths. Therefore, the sum of the numbers is 4.24.