Fractions and Decimals

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Definition:

Definition Fraction -An expression that indicates the quotient of two quantities such as 1/3. www.biotecnika.org

Parts of a Fraction:

Parts of a Fraction Numerator- The number on top of the fraction Denominator- The number on the bottom of the Fraction www.biotecnika.org

Adding or Subtracting Fractions:

Adding or Subtracting Fractions To add or subtract two fractions together you must first find a common denominator.  Example : 1/2 + 1/6 1/2 = 3/6  so, 3/6+ 1/6= 4/6 or 2/3 in simplest form www.biotecnika.org

Adding Fractions:

Adding Fractions www.biotecnika.org

Subtracting Fractions:

Subtracting Fractions www.biotecnika.org

Multiplying Fractions:

Multiplying Fractions Step 1: Simplify the fractions if not in lowest terms.  Step 2: Multiply the numerators of the fractions to get the new numerator.  Step 3: Multiply the denominators of the fractions to get the new denominator.  Step 4: Simplify the resulting fraction if possible. www.biotecnika.org

Example::

Example:

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If 7a =3 and 3b = 7, what is the value of a/b? 9/49 3/7 1 7/3 Example www.biotecnika.org

Decimal Definition:

Decimal Definition A fraction with an unwritten denominator of 10 or some power of ten, indicated by a decimal point www.biotecnika.org

Adding and Subtracting Decimals:

Adding and Subtracting Decimals To add or subtract decimals you must line up the decimals  www.biotecnika.org

Multiplying Decimals:

Multiplying Decimals www.biotecnika.org

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Example 1 Example 2 www.biotecnika.org

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Relationship Between Decimals and Fractions:

Relationship Between Decimals and Fractions Both represent a part of a whole A fraction is based on the number into which the whole is divided(the denominator).  The numerator (the top) is the PART, the denominator (the bottom) is the WHOLE. A decimal is based on the number in terms of tenths, hundredths, thousandths, etc. www.biotecnika.org

Conversions:

Conversions Decimals to Fractions and Fractions to Decimals www.biotecnika.org

How to Convert Decimals to Fractions:

How to Convert Decimals to Fractions Use the place value of the last digit in the number to determine what the denominator of the fraction will be. www.biotecnika.org

How to Convert Decimals to Fractions:

How to Convert Decimals to Fractions .24 www.biotecnika.org

How to Convert Decimals to Fractions:

How to Convert Decimals to Fractions .5 The 5 is in the tenths place 10 5 www.biotecnika.org

How to Convert Decimals to Fractions:

How to Convert Decimals to Fractions .84 The 4 is in the hundredths place 100 84 www.biotecnika.org

What if there is a whole number before the decimal point?:

What if there is a whole number before the decimal point? 1.589 The 9 is in the thousandths place 1000 589 1 www.biotecnika.org

What if there is a whole number before the decimal point?:

25.5 The 5 is in the tenths place 10 5 25 What if there is a whole number before the decimal point? www.biotecnika.org

How to Convert Fractions to Decimals:

How to Convert Fractions to Decimals 100 23 This is the hundredths place so the 3 needs to be in the hundredths place. 2 3 .23 www.biotecnika.org

How to Convert Fractions to Decimals:

How to Convert Fractions to Decimals 1000 567 This is the thousandths place so the 7 needs to be in the thousandths place. 5 6 .567 7 www.biotecnika.org

What if there is a whole number before the fraction?:

What if there is a whole number before the fraction? 1000 567 This is the thousandths place so the 7 needs to be in the thousandths place. 5 6 3.567 7 3 3 www.biotecnika.org

How to Convert Fractions to Decimals:

How to Convert Fractions to Decimals 1000 34 24.034 24 This is the thousandths place so the 4 needs to be in the thousandths place. www.biotecnika.org

Suppose You Can’t Use A Denominator of 10?:

Suppose You Can ’ t Use A Denominator of 10? 6 5 Divide the Numerator by the Denominator www.biotecnika.org

Suppose You Can’t Use A Denominator of 10?:

Suppose You Can ’ t Use A Denominator of 10? 6 5 6 5 .0 . 8 4 8 2 0 0 3 18 2 .83 www.biotecnika.org

Suppose You Can’t Use A Denominator of 10?:

Suppose You Can ’ t Use A Denominator of 10? 3 2 3 2 .0 . 6 1 8 2 .6 www.biotecnika.org

Try Some . . .:

Try Some . . . 8 7 50 5 10 6 4 3 16 12 40 3 www.biotecnika.org

Try Some . . .:

Try Some . . . .35 .25 .95 .6 .875 .125 www.biotecnika.org

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1:

1 When 0.36 is written in simplest fractional form, the sum of numerator and the denominator is: a) 34 b) 45 c) 114 d) 135 Ans : a www.biotecnika.org

2:

2 Which of the following has fractions in ascending order? 1/3, 2/5, 4/7, 3/5, 5/6, 6/7 1/3, 2/5, 3/5, 4/7, 5/6, 6/7 1/3, 2/5, 3/5, 5/6, 4/7, 6/7 2/5, 3/5, 1/3, 4/7, 5/6, 6/7 Ans : a www.biotecnika.org

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3 What is the difference between the biggest and the smallest fraction among 2/3, 3/4, 4/5 and 5/6? a) 1/6 b) 1/12 c) 1/20 d) 1/30 Ans : a www.biotecnika.org

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4 The value of (1+0.1+0.01+0.001) is: 1.001 b) 1.011 c) 1.003 d) 1.111 Ans : d www.biotecnika.org

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5 The number 518000000 when expressed in scientific notation, equals: a) 51.8 x10 6 b) 51.8x10 7 c) 5.18 x10 8 d) 5.18x 10 9 Ans : c www.biotecnika.org

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6 If 1.125 x 10 k = 0.001125, then the value of k is : a) -4 b) -3 c) -2 d) -1 Ans : c www.biotecnika.org

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7 How many digits will be there to the right of the decimal point in the product of 95.75 and 0.02554? a) 5 b) 6 c) 7 d) None of these Ans : c www.biotecnika.org

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8 (0.00625 of 23/5), when expressed as a vulgar fraction, equals: a) 23/80 b) 23/800 c) 23/8000 d) 125/23 Ans : b www.biotecnika.org

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9 0.213/ 0.00213 =? a ) 1 b) 10 c) 100 d) None of these Ans : c www.biotecnika.org

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10 A tailor has 37.5 m of cloth and he has to make 8 pieces out of a meter of cloth. How many pieces can he make out of this cloth? a) 300 b) 360 c) 400 d) None of these Ans : a www.biotecnika.org

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11 The prices of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs . 4.20 and that of Y was Rs . 6.30, in which year commodity X will cost 40 paise more than the commodity Y? a) 2010 b) 2011 c) 2012 d) 2013 Ans : b www.biotecnika.org

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12 If 1/6.198 = 0.16134, then the value of 1/ 0.0006198 is: a) 0.016134 b) 0.16134 c) 1613.4 d) 16134 Ans : c www.biotecnika.org

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13 When 52416 is divided by 312, the quotient is 168. What will be the quotient when 52.416 is divided by 0.0168? 3.12 b) 312 c) 3120 d) None of these Ans : c www.biotecnika.org

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14 Evaluate [(2.39)2 – (1.61)2]/ (2.39 – 1.61) a) 2 b) 4 c) 6 d) 8 Ans : b www.biotecnika.org

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15 What decimal of an hour is a second? a) 0.0025 b) 0.0256 c) 0.00027 d) 0.00126 Ans : c www.biotecnika.org

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16 The expression (11.98 x 11.98 + 11.98 x a + 0.02 x 0.02) will be a perfect square for  a equal to: a) 0.02 b) 0.2 c) 0.04 d) 0.4 Ans : c www.biotecnika.org

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17 What will be the value of: 25.732 2 – 15.732 2 ? a) 214.64 b) 314.64 c) 414.64 d) 412.64 Ans : c www.biotecnika.org

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18 I bought my coat in the January sales with 1/3 off the original price. What percentage was taken off the price of the coat ? a) 56% b) 78% c)33% d)34% Ans : c www.biotecnika.org

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19 [(4.2 x 4.2)-(1.9 x 1.9)]/(2.3 x 6.1) is equal to: a) 0.5 b) 1.0 c) 20 d) 22 Ans : b www.biotecnika.org

20:

20 Given that 268 x 74 = 19832, find the value of 2.68 x .74 . a) 19.832 b)198.32 c)0.19832 d)1.9832 Ans : d www.biotecnika.org

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