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$Use benchmark fractions to estimate sums and differences less than or greater than 1. Write each expression in the correct answer space. Less Than 1 Greater Than I {:[(7)/(8)+(5)/(10),1(5)/(8)-(5)/(6),(10)/(10)-(2)/(3)],[(1)/(2)+(2)/(3),(5)/(12)+(1)/(4),1(1)/(6)+(7)/(8)]:}$

$6$ . Use benchmark fractions to estimate sums and differences less than or greater than $1$ . Write each expression in the correct answer space. $\newline$ \begin{tabular}{|l|l|} $\newline$ \hline Less Than $1$ & Greater Than I \\ $\newline$ \hline & \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ $\begin{array}{lll} \frac{7}{8}+\frac{5}{10} & 1 \frac{5}{8}-\frac{5}{6} & \frac{10}{10}-\frac{2}{3} \\ \frac{1}{2}+\frac{2}{3} & \frac{5}{12}+\frac{1}{4} & 1 \frac{1}{6}+\frac{7}{8} \end{array}$

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Math Problems

Grade 8

Write variable expressions for arithmetic sequences

Full solution

6

. Use benchmark fractions to estimate sums and differences less than or greater than

1

. Write each expression in the correct answer space.

\newline

\begin{tabular}{|l|l|}

\newline

\hline Less Than

1

& Greater Than I \\

\newline

\hline & \\

\newline

\hline

\newline

\end{tabular}

\newline

\begin{array}{lll} \frac{7}{8}+\frac{5}{10} & 1 \frac{5}{8}-\frac{5}{6} & \frac{10}{10}-\frac{2}{3} \\ \frac{1}{2}+\frac{2}{3} & \frac{5}{12}+\frac{1}{4} & 1 \frac{1}{6}+\frac{7}{8} \end{array}

Estimation and Addition: Let's start with the first expression in the ＂Less Than $1$ ＂ column: $(\frac{7}{8}) + (\frac{5}{10})$ . We can estimate $(\frac{7}{8})$ to be close to $1$ , and $(\frac{5}{10})$ to be exactly $\frac{1}{2}$ . Adding these estimates together: $1 + \frac{1}{2} = 1 \frac{1}{2}$ , which is greater than $1$ .
Estimation and Subtraction: Now let's look at the second expression in the ＂Less Than $1$ ＂ column: $1\left(\frac{5}{8}\right) - \left(\frac{5}{6}\right)$ . We can estimate $1\left(\frac{5}{8}\right)$ to be a little more than $1$ , and $\left(\frac{5}{6}\right)$ to be close to $1$ . Subtracting these estimates: a little more than $1$ - close to $1 =$ a little more than $0$ , which is less than $1$ .
Exact Subtraction: For the third expression in the ＂Less Than $1$ ＂ column: $(\frac{10}{10}) - (\frac{2}{3})$ . $(\frac{10}{10})$ is exactly $1$ , and $(\frac{2}{3})$ can be estimated as being close to $\frac{2}{3}$ . Subtracting these estimates: $1 - \frac{2}{3} = \frac{1}{3}$ , which is less than $1$ .
Estimation and Addition: Moving to the ＂Greater Than $1$ ＂ column, let's start with the first expression: $(\frac{1}{2}) + (\frac{2}{3})$ . We can estimate $(\frac{1}{2})$ as $\frac{1}{2}$ and $(\frac{2}{3})$ as being a little more than $\frac{1}{2}$ . Adding these estimates together: $\frac{1}{2} +$ a little more than $\frac{1}{2} =$ a little more than $1$ , which is greater than $1$ .
Estimation and Addition: Now let's look at the second expression in the ＂Greater Than $1$ ＂ column: $(\frac{5}{12}) + (\frac{1}{4})$ . We can estimate $(\frac{5}{12})$ as being a little less than $\frac{1}{2}$ , and $(\frac{1}{4})$ as exactly $\frac{1}{4}$ . Adding these estimates together: a little less than $\frac{1}{2}$ + $\frac{1}{4}$ = a little less than $\frac{3}{4}$ , which is less than $1$ .
Estimation and Addition: For the third expression in the ＂Greater Than $1$ ＂ column: $1(\frac{1}{6}) + (\frac{7}{8})$ . We can estimate $1(\frac{1}{6})$ as being a little more than $1$ , and $(\frac{7}{8})$ as being close to $1$ . Adding these estimates together: a little more than $1 +$ close to $1 =$ more than $2$ , which is greater than $1$ .