what words are used in mathematics to mean subtraction
To begin, you translate English phrases into algebraic expressions. An algebraic expression is a collection of numbers, variables, operations, and grouping symbols. You will translate an unknown number as the variable ten or n. The group symbols are usually a gear up of parentheses, only they can also exist sets of brackets or braces.
In translating expressions, you lot desire to be well acquainted with basic keywords that translate into mathematical operations: addition keywords, subtraction keywords, multiplication keywords, and partitioning keywords, which are covered in the four following sections.
Addition keywords
Some common examples of addition keywords are as follows:
- SUM OF_____ AND _____
- TOTAL OF _____ AND _____
- _____ PLUS _____
- _____ INCREASED Past _____
- GAIN
- RAISE
- More
- Increase OF
The starting time ii keywords (SUM and TOTAL) are called leading keywords because they pb the expression. The second ii keywords (PLUS and INCREASED BY) are keywords that bespeak the exact placement of the plus sign. The last 4 keywords can be institute in word bug and may indicate addition.
When an expression begins with the leading keywords SUM or TOTAL, the leading keyword defines the corresponding AND. The plus sign and then physically replaces the AND in the expression.
Instance i: Translate the following: the sum of five and a number
The post-obit steps help you lot interpret this problem:
1. Underline the words before and after AND when information technology corresponds to the leading keyword SUM OF.
- the sum of v and a number
ii. Circle the leading keyword and point the respective AND that it defines.
3. Translate each underlined expression and supersede AND with a plus sign.
- The expression translates to five + 10.
Example 2: Translate the following: the total of a number and negative iii
Use the following steps to translate this problem:
1. The keyword Total OF is a leading keyword that defines AND, so underline the words before and after AND: "a number" and "negative iii."
- the total of a number and negative three
2. Circle the leading keyword and signal the corresponding AND that it defines.
three. Translate each underlined expression and replace AND with a plus sign.
- The expression translates to x + −3.
Example 3: Interpret the post-obit: the sum of vii and negative 4
Translate this example in the following way:
one. The word SUM OF is a leading keyword that defines AND, so underline the words before and later on AND: "seven" and "negative four."
- the sum of seven and negative four
2. Circle the leading keyword and betoken the respective AND that information technology defines.
3. Interpret each underlined expression and replace AND with a plus sign.
- The expression translates to 7 + −four.
Reminder: The AND keyword translates to hateful "plus" because the leading keyword is SUM OF. With other leading keywords (discussed in the post-obit sections), AND can mean other things. Also notice that y'all do not simplify the expression and get "3" for the answer considering you lot are just translating words into symbols and non performing the math.
2 other keywords on the improver keyword list, PLUS and INCREASED Past, can be correctly translated past the direct translation strategy. In the direct translation strategy, yous translate each give-and-take into its respective algebraic symbol, 1 at a time, in the same society as written, as shown in Example 4.
Example 4: Translate the following: a number increased by 20‐four
- The expression translates to 10 + 24.
Some additional keywords, such equally GAIN, More than, INCREASE OF, and Enhance, are commonly found in story problems, as in Instance 5.
Example 5: Translate the post-obit story problem into a mathematical expression about the weight of the linebacker: The defensive linebacker weighed two hundred 20‐two pounds at the showtime of bound training. He had a proceeds of seventeen pounds afterwards working out with the squad for four weeks.
- The expression translates to 222 + 17.
Note: Non all numbers mentioned in a word problem should exist included in the mathematical expression. The number "iv" is only interesting fact, simply it is not data you demand in guild to write an expression nearly the linebacker'due south weight.
You may as well be wondering why the reply isn't 239 pounds. That's considering the question asks you to translate the story problem into a mathematical expression, not to evaluate the expression.
Case 6: Translate the following give-and-take problem into a mathematical expression about the cashier's current hourly wage: A cashier at the corner grocery was earning $half-dozen.25 an hour. He received a raise of 25 cents an hour.
- The expression translates to 6.25 + 0.25.
Annotation: The hourly wage is stated in dollars, and the heighten is stated in cents. Whatever fourth dimension you are adding two numbers that have units, make sure both numbers are measured with the same units; if they aren't, convert one of the numbers to the same units as the other. Having both numbers measured with the same units is called homogeneous units. In this instance, you convert his heighten, the 25 cents, to $0.25 because his hourly wage is measured in dollars, non cents, and then the raise must likewise exist in dollars.
Subtraction keywords
Subtraction keywords too include leading keywords, keywords that can be translated ane word at a time, and keywords that are found in story problems. Look at the following listing of subtraction keywords:
- DIFFERENCE Between _____ AND _____
- _____ MINUS _____
- _____ DECREASED BY _____
- LOSS
- LESS
- FEWER
- TAKE Abroad
One subtraction keyword (Departure Between) is a two‐part expression that begins with a leading keyword that defines the respective AND. You tin can apply the same methods of underlining and circumvoluted the keywords shown in the preceding department to translate these expressions.
Example 7: Translate the following: the difference between four and 6
Here is how you translate Instance seven:
1. Because the keyword DIFFERENCE Between is a leading keyword that defines the corresponding AND, underline the words before and afterwards AND: "four" and "six."
- the difference between four and half-dozen
2. Circumvolve the leading keyword and indicate the corresponding AND that it defines.
3. Interpret each underlined expression and supervene upon AND with a minus sign.
- The expression translates to 4 – six.
Note: AND is not always translated to mean add-on. Here, the DIFFERENCE Betwixt is the leading keyword that defines the AND to mean subtraction.
Other subtraction keywords, such as MINUS and DECREASED By, use the directly translation strategy. Example viii is a subtraction word problem that is translated one keyword at a time, in the exact lodge of the expression.
Case eight: Translate the post-obit: twenty‐four decreased by a number
- The expression translates to 24 – x.
In a story trouble, you may find the subtraction keywords LOSS, LESS, FEWER, and Have AWAY, as shown in Example 9.
Example 9: Translate the following word problem into a mathematical expression about the electric current value of materials at the chore site: A construction company stored $1,253 worth of materials at the job site. The visitor suffered a loss of $300 due to tempest harm.
- The expression translates to 1,253 – 300.
Multiplication keywords
Some common examples of multiplication keywords are equally follows:
- MULTIPLY _____ Past _____
- PRODUCT OF _____ AND _____
- _____ TIMES _____
- DOUBLE _____
- TWICE _____
- TRIPLE _____
- Per centum OF _____
- FRACTION OF _____
For 2 of the multiplication keywords, MULTIPLY and PRODUCT OF, a leading keyword defines the corresponding BY or AND, equally shown in Example x.
Example ten: Translate the post-obit: the product of vii and a number
Interpret this case in the following mode:
one. Because PRODUCT OF is a leading keyword that corresponds to AND, underline the words before and after AND: "seven" and "a number."
- the product of seven and a number
ii. Circle the leading keyword and indicate the corresponding AND that information technology defines.
iii. Translate each underlined expression and supplant AND with a times sign.
- The expression translates to vii × 10.
Notation: Go on in listen that AND does not always indicate addition. The keyword Production OF defines the AND in this expression to mean multiplication.
A multiplication expression that is translated by the direct translation method is shown in Example 11.
Instance 11: Translate the following: a number times fifteen
The expression translates to x × 15.
Some multiplication keywords, such as DOUBLE, TWICE, and TRIPLE, translate into a number and the operation of multiplication, every bit shown in Examples 12 and 13.
Example 12: Translate the post-obit: twice a number
The expression translates to 2 × x.
Example xiii: Translate the following word problem into a mathematical expression: Jennifer had $15 dollars in the bank. Over the next ii weeks she doubled her money.
The expression translates to 2 × xv.
One of the keywords that indicates multiplication is OF. In give-and-take issues, however, yous may see more than than one use of the word "of." The simply OF that indicates multiplication is the i that follows the keyword Per centum, the percent sign, the keyword FRACTION, or a fraction. Meet Examples 14 and fifteen.
Example xiv: Translate the post-obit: twenty 5 percent of four hundred dollars
The expression translates to 0.25 × 400.
Notation: Remember that a pct is inverse to a decimal before multiplying.
Example 15: Translate the following: one‐third of twenty‐vii
The expression translates to 
Division keywords
Some common examples of segmentation keywords are as follows:
- Quotient OF _____ AND _____
- DIVIDE _____ By _____
- _____ DIVIDED By _____
- DIVIDED EQUALLY
- PER
The keywords Production OF and Caliber OF are difficult for some people to differentiate. Here is a hint to assist you remember which ane indicates division and which i indicates multiplication: Quotient is a "harder" word than "Production," and segmentation is a "harder" operation than multiplication.
Retrieve: Leading keywords define the corresponding AND or BY to hateful divide, ordinarily designated with the symbol ÷.
Example 16: Translate the post-obit: the quotient of seven and a number
1. Considering the keyword Caliber OF is a leading keyword that defines AND, underline the words earlier and after AND: "seven" and "a number."
- the quotient of seven and a number
ii. Circle the leading keyword and indicate the corresponding AND that information technology defines.
three. Translate each underlined expression and supercede AND with a division sign.
- The expression translates to 7 ÷ due north.
Note: Here, the keyword QUOTIENT OF defines AND to mean division.
Instance 17: Translate the following: divide negative 30‐six by nine
one. Considering the word Separate is a leading keyword that defines the BY, underline the words before and after BY: "negative xxx‐6" and "nine."
- divide negative 30‐6 by nine
2. Circumvolve the leading keyword and signal the corresponding Past that it defines.
3. Translate each underlined expression and replace Past with a partition sign.
- The expression translates to
Annotation: The first number goes in the numerator when using a fraction bar to bespeak sectionalization. The number in the numerator (the −36) goes inside the "house" when using the long sectionalization symbol.
Some division keywords can exist translated ane give-and-take at a fourth dimension. Instead, you merely follow the sentence and replace with algebraic notations every bit y'all go forth.
Example 18: Translate the following: a number divided by xvi
The expression translates to 
Often, in story bug, the keyword that indicates sectionalisation is PER. When a story problem asks for the speed of a vehicle in miles per hour, prepare the expression to divide the number of miles by the number of hours. Yous not simply directly translate "miles" ÷ "hours," only besides identify the number of miles and number of hours by finding them elsewhere in the problem. Meet Example 19.
Example 19: Translate the following discussion problem into a mathematical expression near speed: It takes three hours to travel 150 miles to grandmother's business firm. How do yous find your average speed in miles per 60 minutes?
You find "miles" ÷ "hours" in the question. In the beginning part of the word problem, you detect the number of miles, 150 miles, and the number of hours, three hours.
The expression translates to 150 ÷ 3.
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