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Calculate and show your workings for the following: 1) 4.36 + 2/5 + 12.98 2) 16/3 + 100/23 + 7.5 3) 13/5 + 0.57 + 2.14 4) 86/124 - 14/94 5) 94/5 - 37 187 6) 51/56 - 43/6

Mathematics

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Here are the solutions to your problems:

Part 1.1· 1 step

Calculate 4.36+2.5+12.984.36 + 2.5 + 12.98.

  1. Align the decimal points and add the numbers.

    4.362.50+12.9819.84\begin{align*} 4.36 \\ 2.50 \\ + 12.98 \\ \hline 19.84 \end{align*}

    The sum is 19.84.

    19.84\boxed{\textbf{19.84}}

Part 1.2· 1 step

Calculate 16.3+100.23+7.516.3 + 100.23 + 7.5.

  1. Align the decimal points and add the numbers.

    16.30100.23+7.50124.03\begin{align*} 16.30 \\ 100.23 \\ + 7.50 \\ \hline 124.03 \end{align*}

    The sum is 124.03.

    124.03\boxed{\textbf{124.03}}

Part 1.3· 2 steps

Calculate 135+0.57+2.14\frac{13}{5} + 0.57 + 2.14.

  1. Convert the fraction to a decimal.

    135=2.6\frac{13}{5} = 2.6

  2. Add the decimals.

    2.600.57+2.145.31\begin{align*} 2.60 \\ 0.57 \\ + 2.14 \\ \hline 5.31 \end{align*}

    The sum is 5.31.

    5.31\boxed{\textbf{5.31}}

Part 1.4· 1 step

Calculate 86.124−14.9486.124 - 14.94.

  1. Align the decimal points and subtract the numbers.

    Add a zero to 14.94 to match the number of decimal places.

    86.124−14.94071.184\begin{align*} 86.124 \\ - 14.940 \\ \hline 71.184 \end{align*}

    The difference is 71.184.

    71.184\boxed{\textbf{71.184}}

Part 1.5· 1 step

Calculate 94.5−37.18794.5 - 37.187.

  1. Align the decimal points and subtract the numbers.

    Add zeros to 94.5 to match the number of decimal places.

    94.500−37.18757.313\begin{align*} 94.500 \\ - 37.187 \\ \hline 57.313 \end{align*}

    The difference is 57.313.

    57.313\boxed{\textbf{57.313}}

Part 1.6· 3 steps

Calculate 5156−436\frac{51}{56} - \frac{43}{6}.

  1. Find the least common multiple (LCM) of the denominators 56 and 6.

    The prime factorization of 56=23×756 = 2^3 \times 7.
    The prime factorization of 6=2×36 = 2 \times 3.
    The LCM(56,6)=23×3×7=8×3×7=168(56, 6) = 2^3 \times 3 \times 7 = 8 \times 3 \times 7 = 168.

  2. Convert both fractions to equivalent fractions with the common denominator 168.

    5156=51×356×3=153168\frac{51}{56} = \frac{51 \times 3}{56 \times 3} = \frac{153}{168} 436=43×286×28=1204168\frac{43}{6} = \frac{43 \times 28}{6 \times 28} = \frac{1204}{168}

  3. Subtract the fractions.

    153168−1204168=153−1204168=−1051168\frac{153}{168} - \frac{1204}{168} = \frac{153 - 1204}{168} = \frac{-1051}{168}

    The difference is −1051168\frac{-1051}{168}.

    −1051168\boxed{\textbf{$-\frac{1051}{168}$}}

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