Question

thursday
what is the value of the underlined digit.
9.\underline{8} 0.2\underline{4}
solve the equation.
7×d = 14×4
solve the equation.
2 = 174÷j
how can you tell when a fraction is in simplest form?
find the product.
6,208×9
find the quotient.
5,400÷9
find 2 equivalent fractions for each fraction below.
\\(\frac{1}{5}\\) \\(\frac{6}{8}\\)
simplify each fraction.
\\(\frac{4}{20}\\) \\(\frac{8}{16}\\)
simplify each fraction.
\\(\frac{3}{9}\\) \\(\frac{20}{100}\\)

Explanation:

Step1: Find digit values (9.8)

The underlined digit 8 is in the tenths place, so its value is $\frac{8}{10} = 0.8$.

Step2: Find digit values (0.24)

The underlined digit 4 is in the hundredths place, so its value is $\frac{4}{100} = 0.04$.

Step3: Solve $7 \times d = 14 \times 4$

First calculate right-hand side: $14 \times 4 = 56$. Then isolate $d$: $d = \frac{56}{7} = 8$.

Step4: Solve $2 = 174 \div j$

Rearrange to solve for $j$: $j = \frac{174}{2} = 87$.

Step5: Explain simplest fraction form

A fraction is in simplest form when its numerator and denominator share no common positive integer factors other than 1.

Step6: Calculate $6,208 \times 9$

Multiply directly: $6208 \times 9 = 55872$.

Step7: Calculate $5,400 \div 9$

Divide directly: $5400 \div 9 = 600$.

Step8: Find equivalents for $\frac{1}{5}$

Multiply numerator/denominator by 2: $\frac{2}{10}$; multiply by 3: $\frac{3}{15}$.

Step9: Find equivalents for $\frac{6}{8}$

Multiply numerator/denominator by 2: $\frac{12}{16}$; divide by 2 first then multiply by 3: $\frac{9}{12}$.

Step10: Simplify $\frac{4}{20}$

Divide numerator/denominator by GCD 4: $\frac{4\div4}{20\div4} = \frac{1}{5}$.

Step11: Simplify $\frac{8}{16}$

Divide numerator/denominator by GCD 8: $\frac{8\div8}{16\div8} = \frac{1}{2}$.

Step12: Simplify $\frac{3}{9}$

Divide numerator/denominator by GCD 3: $\frac{3\div3}{9\div3} = \frac{1}{3}$.

Step13: Simplify $\frac{20}{100}$

Divide numerator/denominator by GCD 20: $\frac{20\div20}{100\div20} = \frac{1}{5}$.

Answer:

1. Value of underlined digits:

• $9.\underline{8}$: $0.8$
• $0.2\underline{4}$: $0.04$

1. Solved equations:

• $7 \times d = 14 \times 4$: $d=8$
• $2=174\div j$: $j=87$

1. Simplest fraction explanation: A fraction is in simplest form when its numerator and denominator have no common factors other than 1.
2. Product/Quotient:

• $6,208 \times 9 = 55872$
• $5,400 \div 9 = 600$

1. Equivalent fractions:

• $\frac{1}{5}$: $\frac{2}{10}$, $\frac{3}{15}$
• $\frac{6}{8}$: $\frac{12}{16}$, $\frac{9}{12}$

1. Simplified fractions:

• $\frac{4}{20} = \frac{1}{5}$
• $\frac{8}{16} = \frac{1}{2}$
• $\frac{3}{9} = \frac{1}{3}$
• $\frac{20}{100} = \frac{1}{5}$