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Find the absolute value in each of the following expressions.

Mathematics

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6 parts
a

2516\frac{25}{16}

b

43760\frac{437}{60}

c

16435\frac{164}{35}

d
79.115
e

19930\frac{199}{30}

f

338\frac{33}{8}

Step-by-step solution

24 steps

5. Find the absolute value in each of the following expressions.

Part a· 3 steps

38−116+54\frac{3}{8} - \frac{1}{16} + \frac{5}{4}

  1. Find a common denominator, which is 16.

    Convert the fractions.

    38=3×28×2=616\frac{3}{8} = \frac{3 \times 2}{8 \times 2} = \frac{6}{16} 54=5×44×4=2016\frac{5}{4} = \frac{5 \times 4}{4 \times 4} = \frac{20}{16}

  2. Perform the operations.

    616−116+2016=6−1+2016=2516\frac{6}{16} - \frac{1}{16} + \frac{20}{16} = \frac{6 - 1 + 20}{16} = \frac{25}{16}

  3. Find the absolute value.

    ∣2516∣=2516\left|\frac{25}{16}\right| = \frac{25}{16} 2516\boxed{\frac{25}{16}}

Part b

43760\frac{437}{60}

113+234+3151\frac{1}{3} + 2\frac{3}{4} + 3\frac{1}{5}

  1. Convert mixed numbers to improper fractions.

    113=431\frac{1}{3} = \frac{4}{3} 234=1142\frac{3}{4} = \frac{11}{4} 315=1653\frac{1}{5} = \frac{16}{5}

  2. Find a common denominator for $3, 4, 5$, which is 60.

    Convert the fractions.

    43=4×203×20=8060\frac{4}{3} = \frac{4 \times 20}{3 \times 20} = \frac{80}{60} 114=11×154×15=16560\frac{11}{4} = \frac{11 \times 15}{4 \times 15} = \frac{165}{60} 165=16×125×12=19260\frac{16}{5} = \frac{16 \times 12}{5 \times 12} = \frac{192}{60}

  3. Perform the addition.

    8060+16560+19260=80+165+19260=43760\frac{80}{60} + \frac{165}{60} + \frac{192}{60} = \frac{80 + 165 + 192}{60} = \frac{437}{60}

  4. Find the absolute value.

    ∣43760∣=43760\left|\frac{437}{60}\right| = \frac{437}{60} 43760\boxed{\frac{437}{60}}

Part c

16435\frac{164}{35}

−112+110−327-1\frac{1}{2} + \frac{1}{10} - 3\frac{2}{7}

  1. Convert mixed numbers to improper fractions.

    −112=−32-1\frac{1}{2} = -\frac{3}{2} −327=−237-3\frac{2}{7} = -\frac{23}{7}

  2. Find a common denominator for $2, 10, 7$, which is 70.

    Convert the fractions.

    −32=−3×352×35=−10570-\frac{3}{2} = -\frac{3 \times 35}{2 \times 35} = -\frac{105}{70} 110=1×710×7=770\frac{1}{10} = \frac{1 \times 7}{10 \times 7} = \frac{7}{70} −237=−23×107×10=−23070-\frac{23}{7} = -\frac{23 \times 10}{7 \times 10} = -\frac{230}{70}

  3. Perform the operations.

    −10570+770−23070=−105+7−23070=−98−23070=−32870-\frac{105}{70} + \frac{7}{70} - \frac{230}{70} = \frac{-105 + 7 - 230}{70} = \frac{-98 - 230}{70} = \frac{-328}{70}

  4. Simplify the fraction.

    −32870=−328÷270÷2=−16435\frac{-328}{70} = \frac{-328 \div 2}{70 \div 2} = -\frac{164}{35}

  5. Find the absolute value.

    ∣−16435∣=16435\left|-\frac{164}{35}\right| = \frac{164}{35} 16435\boxed{\frac{164}{35}}

Part d79.115

62.15−28.705+45.6762.15 - 28.705 + 45.67

  1. Perform the subtraction.

    62.15−28.705=33.44562.15 - 28.705 = 33.445

  2. Perform the addition.

    33.445+45.67=79.11533.445 + 45.67 = 79.115

  3. Find the absolute value.

    ∣79.115∣=79.115|79.115| = 79.115 79.115\boxed{79.115}

Part e

19930\frac{199}{30}

213+415+1102\frac{1}{3} + 4\frac{1}{5} + \frac{1}{10}

  1. Convert mixed numbers to improper fractions.

    213=732\frac{1}{3} = \frac{7}{3} 415=2154\frac{1}{5} = \frac{21}{5}

  2. Find a common denominator for $3, 5, 10$, which is 30.

    Convert the fractions.

    73=7×103×10=7030\frac{7}{3} = \frac{7 \times 10}{3 \times 10} = \frac{70}{30} 215=21×65×6=12630\frac{21}{5} = \frac{21 \times 6}{5 \times 6} = \frac{126}{30} 110=1×310×3=330\frac{1}{10} = \frac{1 \times 3}{10 \times 3} = \frac{3}{30}

  3. Perform the addition.

    7030+12630+330=70+126+330=19930\frac{70}{30} + \frac{126}{30} + \frac{3}{30} = \frac{70 + 126 + 3}{30} = \frac{199}{30}

  4. Find the absolute value.

    ∣19930∣=19930\left|\frac{199}{30}\right| = \frac{199}{30} 19930\boxed{\frac{199}{30}}

Part f

338\frac{33}{8}

(712+314)−(238+414)\left(7\frac{1}{2} + 3\frac{1}{4}\right) - \left(2\frac{3}{8} + 4\frac{1}{4}\right)

  1. Convert mixed numbers to improper fractions.

    712=1527\frac{1}{2} = \frac{15}{2} 314=1343\frac{1}{4} = \frac{13}{4} 238=1982\frac{3}{8} = \frac{19}{8} 414=1744\frac{1}{4} = \frac{17}{4}

  2. Calculate the sum in the first parenthesis.

    152+134=15×22×2+134=304+134=434\frac{15}{2} + \frac{13}{4} = \frac{15 \times 2}{2 \times 2} + \frac{13}{4} = \frac{30}{4} + \frac{13}{4} = \frac{43}{4}

  3. Calculate the sum in the second parenthesis.

    198+174=198+17×24×2=198+348=538\frac{19}{8} + \frac{17}{4} = \frac{19}{8} + \frac{17 \times 2}{4 \times 2} = \frac{19}{8} + \frac{34}{8} = \frac{53}{8}

  4. Perform the subtraction.

    434−538=43×24×2−538=868−538=86−538=338\frac{43}{4} - \frac{53}{8} = \frac{43 \times 2}{4 \times 2} - \frac{53}{8} = \frac{86}{8} - \frac{53}{8} = \frac{86 - 53}{8} = \frac{33}{8}

  5. Find the absolute value.

    ∣338∣=338\left|\frac{33}{8}\right| = \frac{33}{8} 338\boxed{\frac{33}{8}}
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