fractions
simplifying fractions
simplify each fraction by using the correct greatest common factor (gcf)
a) $\frac{16}{32}$
circle the gcf
4 8 16
simplify
b) $\frac{27}{30}$
circle the gcf
3 6 9
simplify
c) $\frac{18}{21}$
circle the gcf
3 7 9
simplify
d) $\frac{27}{54}$
circle the gcf
3 9 27
simplify
e) $\frac{12}{15}$
circle the gcf
1 3 5
simplify
f) $\frac{30}{40}$
circle the gcf
5 10 15
simplify
g) $\frac{16}{20}$
circle the gcf
2 4 8
simplify

decimal numbers
division
1. estimate and then solve.
a) $25.7 \div 4.9 =$
estimate:
b) $10.9 \div 2.4 =$
estimate:
c) $30.9 \div 10.2 =$
estimate:
2. explain your thought process when estimating the quotient of a division problem.

3. scale by 10 and then solve.
a) $54.4 \div 3.5 =$
b) $93.5 \div 3.2 =$
4. explain how the decimal point moves in a number when scaling by 10.

Question

fractions
simplifying fractions
simplify each fraction by using the correct greatest common factor (gcf)
a) $\frac{16}{32}$
circle the gcf
4 8 16
simplify
b) $\frac{27}{30}$
circle the gcf
3 6 9
simplify
c) $\frac{18}{21}$
circle the gcf
3 7 9
simplify
d) $\frac{27}{54}$
circle the gcf
3 9 27
simplify
e) $\frac{12}{15}$
circle the gcf
1 3 5
simplify
f) $\frac{30}{40}$
circle the gcf
5 10 15
simplify
g) $\frac{16}{20}$
circle the gcf
2 4 8
simplify

decimal numbers
division
1. estimate and then solve.
a) $25.7 \div 4.9 =$
estimate:
b) $10.9 \div 2.4 =$
estimate:
c) $30.9 \div 10.2 =$
estimate:
2. explain your thought process when estimating the quotient of a division problem.

3. scale by 10 and then solve.
a) $54.4 \div 3.5 =$
b) $93.5 \div 3.2 =$
4. explain how the decimal point moves in a number when scaling by 10.

Accepted Answer

### Part 1: Simplifying Fractions (a to g)

#### a) $\boldsymbol{\frac{16}{32}}$
# Explanation:
## Step1: Identify GCF of 16 and 32. GCF is 16.
$\frac{16 \div 16}{32 \div 16}$
## Step2: Divide numerator and denominator by 16.
$\frac{1}{2}$
# Answer: $\frac{1}{2}$ (GCF circled: 16)

#### b) $\boldsymbol{\frac{27}{30}}$
# Explanation:
## Step1: GCF of 27 and 30 is 3.
$\frac{27 \div 3}{30 \div 3}$
## Step2: Divide by 3.
$\frac{9}{10}$
# Answer: $\frac{9}{10}$ (GCF circled: 3)

#### c) $\boldsymbol{\frac{18}{21}}$
# Explanation:
## Step1: GCF of 18 and 21 is 3.
$\frac{18 \div 3}{21 \div 3}$
## Step2: Divide by 3.
$\frac{6}{7}$
# Answer: $\frac{6}{7}$ (GCF circled: 3)

#### d) $\boldsymbol{\frac{27}{54}}$
# Explanation:
## Step1: GCF of 27 and 54 is 27.
$\frac{27 \div 27}{54 \div 27}$
## Step2: Divide by 27.
$\frac{1}{2}$
# Answer: $\frac{1}{2}$ (GCF circled: 27)

#### e) $\boldsymbol{\frac{12}{15}}$
# Explanation:
## Step1: GCF of 12 and 15 is 3.
$\frac{12 \div 3}{15 \div 3}$
## Step2: Divide by 3.
$\frac{4}{5}$
# Answer: $\frac{4}{5}$ (GCF circled: 3)

#### f) $\boldsymbol{\frac{30}{40}}$
# Explanation:
## Step1: GCF of 30 and 40 is 10.
$\frac{30 \div 10}{40 \div 10}$
## Step2: Divide by 10.
$\frac{3}{4}$
# Answer: $\frac{3}{4}$ (GCF circled: 10)

#### g) $\boldsymbol{\frac{16}{20}}$
# Explanation:
## Step1: GCF of 16 and 20 is 4.
$\frac{16 \div 4}{20 \div 4}$
## Step2: Divide by 4.
$\frac{4}{5}$
# Answer: $\frac{4}{5}$ (GCF circled: 4)

### Part 2: Decimal Division (1a to 4)

#### 1a) $\boldsymbol{25.7 \div 4.9}$
# Explanation:
## Step1: Estimate: Round 25.7 to 25, 4.9 to 5. $25 \div 5 = 5$.
## Step2: Solve: $25.7 \div 4.9 \approx 5.24$ (actual: $25.7 \div 4.9 \approx 5.24$)
# Estimate: 5; Solution: $\approx 5.24$

#### 1b) $\boldsymbol{10.9 \div 2.4}$
# Explanation:
## Step1: Estimate: Round 10.9 to 10, 2.4 to 2. $10 \div 2 = 5$.
## Step2: Solve: $10.9 \div 2.4 \approx 4.54$ (actual: $10.9 \div 2.4 \approx 4.54$)
# Estimate: 5; Solution: $\approx 4.54$

#### 1c) $\boldsymbol{30.9 \div 10.2}$
# Explanation:
## Step1: Estimate: Round 30.9 to 30, 10.2 to 10. $30 \div 10 = 3$.
## Step2: Solve: $30.9 \div 10.2 \approx 3.03$ (actual: $30.9 \div 10.2 \approx 3.03$)
# Estimate: 3; Solution: $\approx 3.03$

#### 2. Thought Process for Estimation
# Explanation:
To estimate a decimal division quotient, round the dividend and divisor to compatible whole numbers (e.g., multiples of 5 or 10) and divide. This simplifies calculation and gives a rough idea of the result.
# Answer: Round dividend and divisor to compatible whole numbers, then divide.

#### 3a) $\boldsymbol{54.4 \div 3.5}$ (Scale by 10)
# Explanation:
## Step1: Scale by 10: Multiply numerator and denominator by 10. $54.4 	imes 10 = 544$, $3.5 	imes 10 = 35$.
## Step2: Solve $544 \div 35 \approx 15.54$
# Solution: $\approx 15.54$

#### 3b) $\boldsymbol{93.5 \div 3.2}$ (Scale by 10)
# Explanation:
## Step1: Scale by 10: $93.5 	imes 10 = 935$, $3.2 	imes 10 = 32$.
## Step2: Solve $935 \div 32 \approx 29.22$
# Solution: $\approx 29.22$

#### 4. Decimal Point Movement When Scaling by 10
# Explanation:
When scaling a number by 10, the decimal point moves **one place to the right** (e.g., $5.4 	imes 10 = 54$). This is because multiplying by 10 increases the place value of each digit by a factor of 10.
# Answer: The decimal point moves one place to the right.

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QUESTION IMAGE

Question

Explanation:

Part 1: Simplifying Fractions (a to g)

a) $\boldsymbol{\frac{16}{32}}$

Step1: Identify GCF of 16 and 32. GCF is 16.

Step2: Divide numerator and denominator by 16.

Step1: GCF of 27 and 30 is 3.

Step2: Divide by 3.

Step1: GCF of 18 and 21 is 3.

Step2: Divide by 3.

Answer:

b) $\boldsymbol{\frac{27}{30}}$