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Chapter 1 Whole Numbers 1-9 Solving Word Problems with Whole Numbers The secret to doing word problems successfully is learning to translate a story into the right sort of mathematical operation. Once you've done this translation from story to math, the rest is easy. Word Problems Using Addition Word problems that require addition ask for the total number or sum of some values. The problems don't always use those exact words, but they point to the same meaning — the total amount of something or the sum of some given amounts. Example How many red tiles can you find in these three groups of tiles? There are 4 red tiles in the first group, 5 in the middle group, and just 2 in the third group. The total number of tiles is 4 + 5 + 2 = 11. |  | Of course you could simply count the red tiles, and come up with the same result. But the math we have to do in our modern business, economy, and technology often uses numbers that are much larger than we would care to count. Suppose the numbers of red tiles was actually 400, 500, and 200. You can see that the sum of these three is 1100. If you were to insist upon counting all those tiles, you'd still be here counting tiles when we had left for lunch. Exercises - There are 190 marbles in one box and 48 in another. What is the total number of marbles in the two boxes?
| Ans: 190 marbles + 48 marbles = 238 | - Shana has 3 kids, Val has 2 kids, Jennifer has 4 kids, and Susan has none. How many kids do these friends have between them?
| Ans: 3 kids + 2 kids + 4 kids + 0 kids = 9 kids | - It is 4 miles from Canfield to Placetown, and 3 miles from Placetown to Smithsburg. How far is it from Canfield to Smithsburg, by way of Placetown?
| Ans: 4 miles + 3 miles = 7 miles | - Jacob needs $10 for admission, $5 for lunch and supper, and $25 for transportation. How much money does Jacob need?
| Ans: $10 + $5 + $25 = $40 | - Dave needs to order topsoil for four parts of his yard. He measures each part and finds them to be 10 square feet, 18 square feet, 24 square feet, and 9 square feet. What is the total area that must be covered with topsoil?
| Ans: 10 sq ft + 18 sq ft + 24 sq ft + 9 sq ft = 61 sq ft | Word Problems Using Subtraction Word problems that require subtraction ask for the amount of increase or decrease or the difference between two values. The problems don't always use those exact words, but they point to the same meaning — the amount of increase/decrease of something or the difference between two given amounts. Examples - Benny's hotdog stand served up 340 hotdogs. Benny and his employees ate 14 of them during the day. How many hotdogs were actually sold at Benny's that day?
| Ans: 340 hotdogs – 14 hotdogs = 326 hotdogs | - There are 1840 steps to the top of Macro City's tallest building. Jason has already climbed 480 steps. How many steps remain to the top of the building?
| Ans: 1840 steps – 480 steps = 1360 steps | - Three friends pool their loose change to buy a package of candy. The candy costs 98 cents, but they have only 89 cents among them. How much more cash do they need?
| Ans: 98 cents – 89 cents = 9 cents | - A quart of milk serves six people. Four people have taken their portion. How many more people can be served?
| Ans: 6 servigs – 4 servings = 2 servings | - The driving distance from Peaceberg to Crosley is 340 miles. A driver making the trip from Peacebert to Crosley sees a road sign that says "Crosley 32 mi." How far has the driver already traveled?
| Ans: 340 miles – 32 miles = 308 miles | 1-9.3 Word Problems Using Multiplication Word problems that should use multiplcation generally ask the the total number or amount of something, given some number of identical groups or amounts. Example How many tiles are in this figure? Of course you could simply count them — 1, 2, 3, and so on. Or you could count the number of tiles along the top (5 of them) and along the side (4 of them), and then multiply: 5 x 4 = 20. |  | Example What is the total number of tiles in this figure? Since there is the same number of tiles in each group, you can determine the total number of tiles by multiplying the number of tiles in each group (20) by the number of groups (4): 20 tiles per group x 4 groups = 80 tiles. Or you could simply spend several minutes counting them individually. |  | Exercises - A certain recipe calls for 2 cups of milk. If you are tripling the recipe, how many cups of milk are required?
| Ans: 2 cups x 3 = 6 cups | - There are 4 dozen fresh eggs in the cooler. How many eggs does this represent?
| Ans: 4 dozen x 12 eggs/dozen = 48 eggs | - A bug is crawling across the floor at the rate of 2 inches per second. How far will be bug crawl in 1 minute?
| Ans: 2 inches per second x 60 seconds = 120 inches | - The hotel can provide 8 conference rooms that have a capacity of 50 people per room. How many people can the hotel accomodate with these eight rooms?
| Ans: 8 rooms x 50 people per room = 400 people | - Each bag of mulch covers an area of 10 square feet. How much area can 12 bags cover?
| Ans: 10 square feet per bag x 12 bags = 120 square feet | \ Word Problems Using Division Word problems that require division ask how things are divided among a given number of groups. Exercises - Four friends agree to equally divide payments on a motocycle costing $12,448. How much does each one pay?
| Ans: $12,448 ÷ 4 people = $3112 per person | - Kate hiked 60 miles in 3 days. How far did she hike each day?
| Ans: 60 miles ÷ 3 days = 20 miles per day | - ABC company has a contract to produce 15,000 widgets each month. If the plant operates 20 days per month, how many widgets should it produce each day?
| Ans: 15,000 widgets ÷ 20 days = 750 widgets per day | - Eighteen slices of pizza are to be divided among four people. How many pieces does each person get?
| Ans: 18 pieces ÷ 4 people = 4 pieces, with 2 pieces left to argue over | - Eric need 48 screws to build a large cabinet. The screws are available at Home Depot in packages of 8. How many packages does Eric need to buy?
| Ans: 48 screws ÷ 8 screws per package = 6 packages |
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