Question

Drag the tiles to the correct boxes to complete the pairs.
Let A = 2, B = 2/5 and C = 3/8
. Find the value of each expression below.
1 7/40 1 3/20 2 1/40 1 39/40
A - B + C
arrowBoth
A × C + B
arrowBoth
A × B + C
arrowBoth
A + B - C

Answer 1

To solve the expressions using the values \( A = 2 \), \( B = \frac{2}{5} \), and \( C = \frac{3}{8} \), we can compute each expression step-by-step:

1. **Find \( A - B + C \)**:
\[
A - B + C = 2 - \frac{2}{5} + \frac{3}{8}
\]
First, convert \( 2 \) to a fraction with a common denominator. The least common multiple of \( 1 \), \( 5 \), and \( 8 \) is \( 40 \).
\[
2 = \frac{80}{40}, \quad \frac{2}{5} = \frac{16}{40}, \quad \frac{3}{8} = \frac{15}{40}
\]
Now substitute:
\[
A - B + C = \frac{80}{40} - \frac{16}{40} + \frac{15}{40}
\]
\[
= \frac{80 - 16 + 15}{40} = \frac{79}{40} \approx 1.975 = 1 \frac{39}{40}
\]

2. **Find \( A \times C + B \)**:
\[
A \times C + B = 2 \times \frac{3}{8} + \frac{2}{5}
\]
First, calculate \( 2 \times \frac{3}{8} \):
\[
= \frac{6}{8} = \frac{3}{4}
\]
Now, find a common denominator for \( \frac{3}{4} \) and \( \frac{2}{5} \). The least common multiple of \( 4 \) and \( 5 \) is \( 20 \):
\[
\frac{3}{4} = \frac{15}{20}, \quad \frac{2}{5} = \frac{8}{20}
\]
Now substitute:
\[
A \times C + B = \frac{15}{20} + \frac{8}{20} = \frac{23}{20} = 1 \frac{3}{20}
\]

3. **Find \( A \times B + C \)**:
\[
A \times B + C = 2 \times \frac{2}{5} + \frac{3}{8}
\]
Calculate \( 2 \times \frac{2}{5} \):
\[
= \frac{4}{5}
\]
Now find a common denominator for \( \frac{4}{5} \) and \( \frac{3}{8} \). The least common multiple of \( 5 \) and \( 8 \) is \( 40 \):
\[
\frac{4}{5} = \frac{32}{40}, \quad \frac{3}{8} = \frac{15}{40}
\]
Now substitute:
\[
A \times B + C = \frac{32}{40} + \frac{15}{40} = \frac{47}{40} = 1 \frac{7}{40}
\]

4. **Find \( A + B - C \)**:
\[
A + B - C = 2 + \frac{2}{5} - \frac{3}{8}
\]
As before, convert \( 2 \) to a fraction:
\[
2 = \frac{80}{40}, \quad \frac{2}{5} = \frac{16}{40}, \quad \frac{3}{8} = \frac{15}{40}
\]
Now substitute:
\[
A + B - C = \frac{80}{40} + \frac{16}{40} - \frac{15}{40} = \frac{81}{40} \approx 2.025 = 2 \frac{1}{40}
\]

Now, let’s match each expression with its result:
- \( A - B + C = 1 \frac{39}{40} \)
- \( A \times C + B = 1 \frac{3}{20} \)
- \( A \times B + C = 1 \frac{7}{40} \)
- \( A + B - C = 2 \frac{1}{40} \)

The completed pairs are:

- \( A - B + C \) → \( 1 \frac{39}{40} \)
- \( A \times C + B \) → \( 1 \frac{3}{20} \)
- \( A \times B + C \) → \( 1 \frac{7}{40} \)
- \( A + B - C \) → \( 2 \frac{1}{40} \)