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Solutions and Explanations to Questions on Fractions - Grade 5

Solutions and explanations to grade 5 fractions questions are presented.


  1. Use any whole number n to write 1 as a fraction as follows:
    n=1, 1=11
    n=2, 1=22
    n=11, 1=1111
    and so on
    NOTE that we cannot write 1=00.
    NOTE that a fraction cannot have a denominator equal to zero.


  2. Any whole number n may be written as a reduced fraction as follows: n1 Hence 5 may be written as 51


  3. When adding fractions, it is important to have a common denominator. In this case, both fractions have a denominator of 4, so we can add the numerators directly. The sum of the numerators gives us the numerator of the resulting fraction. The denominator remains the same. So, the resulting fraction is 14+24=1+24=34


  4. When subtracting fractions, it is important to have a common denominator. In this case, both fractions have a denominator of 7, so we can subtract the numerators directly. The difference between the numerators gives us the numerator of the resulting fraction. The denominator remains the same. So, the resulting fraction is 4727=427=27


  5. 15+23= To add the fractions, we need to follow these steps:
    Step 1: Find a common denominator.
    In this case, the denominators are different (5 and 3). To find a common denominator, we can multiply the denominators together:
    5×3=15
    Step 2: Rewrite the fractions so that they have the same denominator. To make the denominators equal to 15, we need to scale the fractions accordingly.
    We multiply the numerator and denominator of 15 by 3, and the numerator and denominator of 23 by 5:
    15=15×33=315
    23=23×55=1015
    Now, both fractions have the same denominator of 15.
    Step 3: Add the adjusted fractions. We can now add the adjusted fractions:
    315+1015=3+1013=1315
    Therefore, the sum of
    15+23=1315


  6. To add the mixed numbers 312 and 513, we can follow these steps:
    Step 1: Analyze the whole parts of 312 and 513.
    The whole part of 312 is 3, and the whole part of 513 is 5.
    Step 2: Analyze the fractions: The fraction part of 312 is 12 and the fraction part of 513 is 13
    Step 3: Add the whole parts.
    We add the whole parts together: 3+5=8
    Step 4: Add the fraction parts: 12+13
    Step 5: Find a common denominator.
    To add the fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 2 and 3 is 6.
    Step 6: Multiply (adjust) the fractions to have a common denominator of 6:
    12=12×33=36
    13=13×22=26
    Step 7: Add the fractions.
    We add the adjusted fractions together:
    12+13=36+26=56
    Step 8: Put all together.
    312+513=(3+5)+12+13=8+56


  7. The total time for Julia to be ready for school is
    12 hour+14 hour=(12+14) hour
    Write fractions with the same denominator
    12+14=12×22+14=24+14=34 hour.


  8. It is easier to compare fractions if they are written with the same denominator
    A)
    52 and 25 with same denominator become
    52=52×55=2510
    25=25×22=410
    Therefore 52 and 25 are not equivalent
    B)
    Write 43 with denominator 8 as follows
    43=43×22=86
    Therefore 43 and 86 are equivalent
    The fractions in parts C) and D) already have the same denominators and are not equivalent.
    Conclusion: Fractions 4/3 and 8/6 are equivalent because when written with common denominator both denominators and numerators are equal.


  9. To subtract the mixed numbers 523 and 312, we follow these steps:
    Step 1: Convert the mixed numbers to improper fractions.
    523=5+23=533+23=153+23=173
    and
    312=3+12=322+12=62+12=72,
    Step 2: Find a common denominator to the 2 fractions: The denominators of the fractions are 3 and 2, which are different. To find a common denominator, we multiply them: 3×2=6.
    Step 2: Write the fractions with a common denominator.
    173=173×22=346
    72=72×33=216,
    Step 4: Subtract the adjusted fractions.
    523312=346216=136
    Step 5: Reduce (if possible) and convert the improper fraction back to a mixed number (if desired).
    136 cannot be reduced but can be written as a mixed number
    136=12+16=126+16=216


  10. John ate more than Billy and the difference is given by
    123114=(11)+(2314)=(2314)
    Write fractions with the same denominator
    23=23×44=812
    14=14×33=312
    The difference is
    123114=812312=512
    John ate 512 of a pizza more than Billy.


  11. To divide two fractions, you multiply the first one by the multiplicative inverse of the second
    The multiplicative inverse of fraction ab is the fraction ba
    Change the division of two fractions into a multiplication as follows
    52÷34=52×43=5×42×3=206
    The result is an improper fraction and may be written as a mixed number as follows:
    206=18+26=186+26=3+26
    The fraction 26 may be reduced by dividing its numerator and denominator by 2
    26=2÷26÷2=13
    Finally
    52÷34=313


  12. To divide two fractions, you multiply the first one by the multiplicative inverse of the second
    5÷17=51×71=5×71×1=351=35


  13. Multiply numerators together and denominators together.
    25×37=2×35×7=635


  14. Write the given equation
    a+134=2
    Subtract 134 from both sides of the equation
    a+134134=2134
    Simplify to obtain
    a=2134
    Simplify the right side
    =2134
    Simplify
    134
    Rewrite 1 as a fraction 44
    =4434=14
    Hence
    a=1/4


  15. There are two whole shaded items above and one shaded at 34. Hence the mixed number
    234 represents the shaded parts.


  16. False: 212 is a mixed number and is equal to
    212=2+12


  17. Let us say she worked n hour on Friday. The total (addition) for the 5 days is 15 hours. Let us add all hours for 5 days
    312+4+216+112+n=15
    Add whole numbers together and fractions together
    (3+4+2+1)+(12+16+12)+n=15
    Simplify the expressions within the brackets on the left side
    10+(1+16)+n=15
    Which also simplifies to
    11+16+n=15
    Subtract 11+16 from both sides of the above equation
    11+16+n1116=151116
    Simplifies the left and the right sides to obtain
    n=416 Rewrite 4 as a fraction with denominator 4
    n=16416
    n=154
    It is an improper fraction that can be written as a mixed number
    n=154=12+34=334
    Tina worked 3 and 34 hours on Friday.


  18. Write 1710 in decimal form as follows
    1710=1+7÷10=1+0.7=1.7 and corresponds to point W.
    1.7 and corresponds to point W on the graph.


  19. Write mixed number as a sum of a whole part and a fractional part
    213=2+13
    Write 2 as a fraction with denominator 3
    =21×33+13
    Simplify
    =63+13
    Add fractions with common denominator
    =73
    213 as an
    213=73


  20. Divide 31 by 8 to obtain a quotient equal to 3 and a remainder equal to 7 which can be written as
    31=3×8+7
    Hence we can write that
    318=3×8+78=3×88+78
    Simplify
    =3+78=378
    318 as a mixed number is equal to 378


  21. 3×14 may be written as
    3×14=(1+1+1)×14
    Use distribution
    =14+14+14


  22. 314 is a mixed number with a whole part equal to 3 and a fractional part equal to 14 and is written as
    314=3+14


  23. Rewrite the two fractions with the same denominator. The same denominator is the lowest common multiple (LCM) of 5 and 8. First list the first few multiples of 5 and 8 until we obtain a common multiple
    factors of 5:   5, 10, 15, 20, 25, 30, 35, 40, ...
    factors of 8:   8, 16, 24, 32, 40, ...
    The LCM of 5 and 8 is 40
    Rewrite the two fractions with the same denominator 40 (which is the LCM)
    25=25×88=1640
    38=38×55=1540
    1640 is greater than 1540 and therefore 25 is greater than 38 and therefore the above statement is true.


  24. The fraction 76 has its numerator greater than its denominator and hence it is greater than 1.
    The remaining 3 fractions 35,13 and 49 have their numerators smaller than their denominators and are therefore all less than 1. They can be compared by first writing them with the same denominator.
    The same denominator may be the lowest common multiple of their denominators 5, 3 and 9.
    factors of 5:   5, 10, 15, 25, 30, 35, 40, 45,...
    factors of 3:   3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,...
    factors of 9:   9, 18, 27, 36, 45,...
    The lowest common multiple of the denominators 5, 3 and 9 is 45. Hence we rewrite the three fractions with the common denominator 45 as follows:
    35=35×99=2745
    13=13×1515=1545
    49=49×55=2045
    Using the above fractions, we now order the given fractions from least to greatest as follows
    13,49,35,76


  25. 23 of 4 is equal to:
    23×4=23×41=2×43×1
    Simplify
    =83
    Write 8 as 6 + 2. (6 is a multiple of 3)
    =6+23
    Rewrite as a sum of fractions
    =63+23
    Simplify
    =2+23=223
    Hence 23 of 4 as a mixed number is equal to
    223


  26. One hour is equal to 60 minutes. Hence 23 of an hour is equal to
    23×60
    Rewrite 60 as a fraction 601
    =23×601
    Multiply fractions and simplify
    =2×603×1=1203
    Rewrite fraction as a division and simplify
    =120÷3=40 minutes
    Conclusion: Hence 23 of an hour is equal to 40 minutes.


  27. The large square is divided into 16 small squares. Hence every small square is 116 of the large square.
    red: 4 small squares represent 4×116=416=14 of the large square
    blue: 1 small square represents 1×116=116 of the large square
    orange: half a small square represents 12 of 116 = 12×116=132 of the large square
    green: 1 small square and 1/2 of a small square represents 116+12×116
    Simplify
    =116+132
    Rewrite the fraction 116 with denominator 32
    =116×22+132
    Simplify
    =332 of the large square
    black: 3 small squares represent 3×116=316 of the large square
    yellow: 3 small squares represent 3×116=316 of the large square
    We can write the color with the corresponding fractions as follows:
    red: 14 , blue: 116 , orange: 132 , green: 332 , black: 316 , yellow: 316


More References and links

Fractions
Primary Maths (grades 4 and 5) with Free Questions and Problems With Answers
Middle School Maths (grades 6,7,8 and 9) with Free Questions and Problems With Answers

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