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1 st Semester Review

1 st Semester Review. Regular Math. Changing a Fraction to a Decimal. Look at the denominator to see if you can change it to a power of ten (10, 100, 1000, etc…) If you can change * If you cannot change the

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1 st Semester Review

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  1. 1st Semester Review Regular Math

  2. Changing a Fraction to a Decimal • Look at the denominator to see if you can change it to a power of ten (10, 100, 1000, etc…) • If you can change * If you cannot change the the denominator, then also denominator then divide the change the numerator by numerator by the denominator multiplying it by the same factor used to change the denominator. D N

  3. Fraction to a decimal Stephanie bought a basketball on sale for $15, which was 20 % off the original price. What decimal represents the discount she received? F 0.05 G 0.15 H 0.20 J 0.50

  4. Changing a Fraction to a Percent • Percentage is out of 100, so if possible change the denominator to 100. • Change the numerator by multiplying it by the same factor that was used to change the denominator to 100. • The numerator will be the percent. • If you cannot change the denominator to 100 then you will need to divide the numerator by the denominator and then multiply it by 100.

  5. Fractions to Percents By the end of August, the school counselors had completed 12 out of every 16 student requested schedule changes. What percentage of the schedule changes had NOT yet been completed? A 75% B 66% C 28% D 25%

  6. Proportions • Two equivalent ratios • Boys1224 • Girls 16 32

  7. Proportions Josie’s horse eats about 2 bales of hay every 5 days. About how many bales of hay does Josie’s horse eat in 31 days? A 8 B 12 C 16 D 78 The ratio of red rosebushes to yellow rosebushes in the school garden is about 3 to 4. If there were 36 yellow rosebushes, about how many red rosebushes would there be? F 36 G 32 H27 J 12

  8. Proportions To make his family’s favorite chili, Bolivar combines 2 tablespoons of chili powder for every 12 ounces of ground meat. To feed everyone, Bolivar will cook 3 pounds of ground meat. How many tablespoons of chili will he need? A 6 B 8 C 12 D 16 Mrs. Miller is baking cookies for 16 children. She has baked 2 dozen cookies. If she wants each child to receive exactly 2 cookies and have no cookies left over, how many more cookies should she bake? F 1.5 G 8 H 24 J 32

  9. Adding Subtracting Fractions • If the denominators are the same, add or subtract the numerators and simplify if necessary. • If the denominators are not the same, find a common denominator. • After you have found a common denominator multiply the numerator by the same factor that they denominator was multiplied with to change to the common denominator. • Add or Subtract • Simplify

  10. Adding and Subtracting Fractions

  11. Multiplying Fractions • Change all mixed numbers to improper fractions Example: 2 • Change whole numbers to fractions by putting the whole number over one. Example: 16 • Multiply numerator by numerator, and denominator by denominator Example: x = • Simplify if needed, change improper fractions to mixed numbers or whole numbers.

  12. Multiplying Fractions

  13. Multiplying Fractions • Marissa wants to cover her entire wall in paper. She needs for the length to be 5 yards and her width to be 3 yards. How many square yards of paper will Marissa need? • Mr. Gardino uses 6 pieces of lumber that are cut into 12 lengths of inches for decorative borders. If he puts 6 boards end to end, what would be the length of the boards?

  14. Dividing Fractions with a common denominator • Change mixed numbers to improper fractions • Find a common denominator, make sure to change the numerator if you changed the denominator. • Divide the numerators. • Simplify. • Example: 1 ÷ ÷ ÷ 15 ÷ 8 = 1

  15. Dividing Fractions using the reciprocal • Change mixed numbers to improper fractions. • Find the reciprocal (flip) of the second fraction. • Change ÷ to x. • First fraction stays the same. • Solve/Simplify • Example: 1 ÷ ÷ x = or 1

  16. Dividing Fractions Which expression can be used to find the maximum number of 0.2-meter lengths of rope that can be cut from a 6.5-meter length of rope? F 0.2 ÷ 6.5 G 0.2 + 6.5 H 6.5 ÷ 0.2 J 6.5 × 0.2

  17. Dividing Fractions Solve: 2 ÷ 9 ÷ ÷ 1 ÷ 1 ÷ 4

  18. Adding and Subtracting Decimals • Line up the place values, then add or subtract. Marla and three of her friends ordered a $9.99 pizza to share for lunch. Each person also ordered a $1.25 drink. Before tax and tip, how much would each person owe for their meal? A $14.99 B $11.24 C $3.75 D $2.81

  19. Multiplying Decimals • Use fractions- change decimals to place value fractions then multiply across. • Place Value Shift • Multiply as whole numbers • Count place values after the decimal in all factors. • The total number of place values is how many place value shifts to the left in the product.

  20. Multiplying Decimals Carlos ran 1.3 miles each day for 3 days, 2.1 miles each day for 2 days, and 0.8 miles for one day. How many total miles has Carlos run? A 8.9 miles C 4.2 miles B 6.8 miles D 3.4 miles Joaquin bought one pair of athletic shoes for $79.99, one team jersey for $39.49, and three bobble-head toys for $7.59 each. How much did Joaquin spend, not including tax? A $142.25C $119.48 B $141.95 D $27.47

  21. Dividing Decimals • Use fractions- change decimals to place value fractions. Find a common denominator if necessary, then divide across. • Place value shift • Shift the decimal in the divisor in order to create a whole number. Shift the decimal in the dividend the same number of places. Then use long division. • Multiply by the reciprocal • Keep the first fraction the same. • Change division sign to multiplication sign • Flip the second fraction (reciprocal)

  22. Dividing Decimals Solve: 0.55 ÷ 0.5 = 1.2 ÷ 0.03 =

  23. Finding an Equation A candy company packages their product in three different-sized bags. The small bag of candies contains half as many pieces as the medium bag of candy. The medium bag of candy contains half as many pieces as the large bag of candy. The large bag contains 100 pieces of candy. How many pieces of candy are in the small bag? A 25; because (100÷2)÷ 2 B 400; because (100x2) x 2 C 96; because (100-2) - 2 D104; because (100+2) + 2

  24. Finding an Equation Reese and Cannon solved the problem below. Who is correct with the correct justification? Larry participated in a marathon. He ran twice as much as he walked, and walked four times more than he rested. If he rested for a total of 15 minutes, how many minutes did he spend running? A Reese: 60 minutes because (2)15=30 & (30)2=60. B Reese: 120 minutes because (4)15=60 & (60)2=120. C Cannon: 30 minutes because (2)15=30. D Cannon: 60 minutes because (4)15=60.

  25. Unit Rates • A rate is a ratio that compares quantities measured in different units (miles to hours, miles to gallons) • 120 miles in 3 hours • A unit rate is the rate for one unit of a given quantity (miles per hour, miles per gallon) • 120 miles in 3 hours is 60 miles per(one) hour.

  26. Unit Rates Tom paid $24 for 3 pounds of chocolate fudge. How much did he pay per pound? Stan road his bike 15 miles in 2 hours. How fast was Stan riding his bike per hour?

  27. Converting Hours to Minutes How would you write 5 ½ hours as a combination of hours and minutes? How would you write 10 hours as a combination of hours and minutes?

  28. L N 65° 25° M P Complementary and Supplementary Angles • Complementary angles are two angles whose measures have a sum of 90°. • 65° + 25° = 90° • LMN and NMP are complementary.

  29. K 65° 115° G J H Complementary and Supplementary Angles Supplementary angles are two angles whose measures have a sum of 180°. 65° + 115° = 180° GHK and KHJ are supplementary.

  30. Complementary and Supplementary Angles • The angles are supplementary. What are the missing values? • 145° + s = 180° • 125° + 2 = 180° • The angles are complementary. What are the missing values? • 65° + d = 90° • 71° + m= 90°

  31. Part n Part 67 = Whole Whole 90 100 Percent of a number • Recall that a percent is a part of 100. You can set up and solve a proportion to find the answer. So 67% as a proportion would look like this: • You can also use a percent bar: • http://learnzillion.com/lessons/3447-solve-ratio-and-percent-problems-using-bar-models

  32. Percent of a number • Find the percent of each number: • 30% of 50 • 40% of 40 • Find the amount of the discounted percent: • 15% discount of $78.00 • 25% discount of $64.00

  33. Corresponding angles E B 82◦ 82◦ D 43◦ 55◦ F 43◦ 55◦ A C Corresponding sides Scale Factor/ Similar Factors • Matching sides of two or more polygons are called correspondingsides, and matching angles are called corresponding angles.

  34. SIMILAR FIGURES • Two figures are similar if • The measures of their corresponding angles are equal. • The ratios of the lengths of the corresponding sides are proportional.

  35. Similar Figures Rectangles A and B are similar. What is the length of rectangle B? B 12 ft 3 ft A 5 ft

  36. Similar Figures A Line segment DE is parallel to line segment CB. What is the length of line segment DE? 4 2 E D 4 2 C B 6

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