(Jason Raish for The Washington Post)

What if I told you there’s a new way to use coupons that’s easy and can save you 50 percent or more on your groceries? The average family of four spends as much as $15,364 annually on groceries, according to the U.S. Agriculture Department, so that’s a potential savings of more than $7,500.

I know what you’re thinking: The thought of spending Sundays madly cutting out tiny scraps of paper only to lose them before you can use them is maddening. But please, keep reading!

“A new wave of couponing is taking the world by storm,” said Stephanie Nelson, founder of CouponMom.com. “If shoppers learn some simple strategies, they can cut their grocery bill in half.”

Here are the keys to the new couponing:

1. Never use a coupon by itself; always combine it with other offers.

2. Never try coupon combinations by yourself; use technology to assist you.

Never use a coupon by itself

It’s hard to get excited about saving 50 cents on a $2 package of lunchmeat. That’s what couponing novices do. But what if you could get that lunchmeat for free — and the store even paid you a penny to take it? That’s the power of combining coupons with other offers. Yes, you can do that! In this real-life example, available right now at a store near me, you can take advantage of a store sale plus an Internet coupon plus a cash-back offer. Net result? You get the lunchmeat for free plus 1 cent back.

Here are the most common kinds of coupon combinations. (Don’t worry; there are websites that will help you identify them — more on that later.)

Manufacturer’s coupon + sale: Manufacturers often promote their products in waves, first with coupons, then with sales in specific stores. Hang on to the coupon until the sale begins, and you can take advantage of both at once and deepen your discount.

Manufacturer’s coupon + store coupon: Because one offer comes from the manufacturer and the other from the store, you are allowed to combine them. Note: Drugstores offer more store coupons than grocery stores.

BOGO + two coupons: When a store advertises that a product is “buy one, get one free,” or BOGO, it usually means that both products are half price. Many stores will then let you use two additional coupons, one on each product. For example, I spotted a BOGO deal on dishwasher detergent that made the price of each box $3. Then I spotted separate coupons for $3 off per box of detergent. By layering those on top of the BOGO deal, I got two boxes of detergent for free.

X off Y purchase + other coupons: This strategy refers to the kinds of coupons that offer, for example, $10 off a $40 purchase. You can combine that first coupon with other coupons. The key is to hand the coupons to the cashier in the right order. Use the X-off-Y coupon first, while your total is still high enough to count — $40 in this example. Then hand over your other coupons after that.

Coupon + sale + cash back: Several apps offer cash back on grocery purchases. See details about them below. You can earn cash back even if you got the product on sale and/or used a coupon to buy it. This is what I did, above, in the lunchmeat example.

Make technology do the work for you

If identifying all of these creative coupon combinations sounds exhausting, never fear. There are all sorts of websites and apps that search for combinations for you. Here are several layers of assistance. You can try them all or stop when you’re satisfied with your savings.

Matching websites: CouponMom.com, Nelson’s site, names all the weekly sale items at most grocery stores, drugstores and big-box stores and then lists coupons and cash-back offers available for those same items. The site includes Internet coupons, but it originally revolutionized couponing by telling shoppers which advertising insert contains what paper coupons. That way, instead of mindlessly clipping coupons as you receive the ad inserts, you can simply save the intact inserts and cut coupons only as you see them matched with sales. Some offers still exist only on paper, so if you want the absolute maximum savings, you will include paper coupons. Two other sites that match sales and coupons in a more casual way are Becentsable (becentsable.net) and the Krazy Coupon Lady (thekrazycouponlady.com). Still don’t see your store listed? Search the store name and the term “coupon blogger,” and you’re likely to find a coupon expert to follow.

Printable coupons: Several websites link you to coupons that you can print online, including CouponMom.com, Coupons.com, RedPlum.com and SmartSource (smartsource.com). Additionally, many manufacturers have “printables” right on their own websites. Bonus tip: Often manufacturers let you print a coupon twice. Simply hit the “back” arrow on your computer and print the coupon again.

Store apps: Most grocery chains and also big-box stores such as Target now have their own apps that allow you to load digital coupons and special offers right onto your store loyalty card. Better yet, you don’t have to carry the card anymore, because it’s built into the app. You can even look for deals and load them at the last minute while you’re in the store shopping.

Cash-back apps: Checkout 51, Ibotta, Mobisave and SavingStar all offer cash back for buying certain groceries. You either scan a bar code or take a picture of your receipt to make your claim. You can redeem your cash via Paypal, Venmo or gift cards, depending on the app.

Once you’ve got the hang of modern couponing, then you can layer on one last strategy — if you’ve got the space — that works for all nonperishable goods. Anytime you score a deeply discounted product, stockpile enough to get you through to the next sale. “This strategy is counterintuitive,” said Nelson, “but you can save a lot of money by buying products when they are deeply discounted instead of when you need them.”

Elisabeth Leamy is a 13-time Emmy winner and 25-year consumer advocate for programs such as “Good Morning America” and “The Dr. Oz Show.” Connect with her at leamy.com and @ElisabethLeamy.