Question

1. estimate: 1 3/4 - 2/5

a. about 1
b. about 1 1/2
c. about 1 1/4
d. about 2
extension: draw a model (fraction bars or circles) to represent one subtraction problem above.

Explanation:

Step1: Convert mixed number to improper fraction

$1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4}$, and $\frac{2}{5}$ remains as it is.

Step2: Find a common denominator

The common denominator of 4 and 5 is 20. So, $\frac{7}{4}=\frac{7\times5}{4\times5}=\frac{35}{20}$ and $\frac{2}{5}=\frac{2\times4}{5\times4}=\frac{8}{20}$.

Step3: Subtract the fractions

$\frac{35}{20}-\frac{8}{20}=\frac{35 - 8}{20}=\frac{27}{20}=1\frac{7}{20}\approx1.35$.
Now, estimate each option:

• Option A: $1\approx1.00$
• Option B: $1\frac{1}{2}=\frac{3}{2}=1.50$
• Option C: $1\frac{1}{4}=\frac{5}{4}=1.25$
• Option D: $2 = 2.00$

Since $1.25$ (Option C) is closest to our calculated result of approximately $1.35$.

Answer:

C. About $1\frac{1}{4}$